
k 


PrllCLASSIFIED 
By authority Secretary of 


OCT Itl 1960 


Defense memo^ August i960 

library of congress 






SUMMARY TECHNICAL REPORT 
OF THE 

NATIONAL DEFENSE RESEARCH COMMITTEE 

;:*• 

DECLASSIFIED 
By authority Secretary of 

OCT ly 1960 


Defense memo 2 August 1960 

RE^^^If.^nLASSmCATlON 


Th 


Aj^nt cont|iiiafinfopmation affecting tm- national defense of the United 


i or the revelation of 
tntiiittifecrDy Taw. 


I hij^lume is' 

^s of the Wal 
rial which was 

ancri\aw4i £ene i(^~ 
of any material. 




and 32, as amended. 


Utt-aiiy_iQamie r 


ikUthor- 


assified CONFIDENTS 
nd Navy Department;^ 
NFIDENTIAL ^ 

gsifina-tion-ftr^^nr, 

the r*:; 


m,.a€CortiarfoM(i**rn^§eG4^^ re gujaa 
luse ^ryaiif™aptcrs,f»irtaairrm 

>rinti|l%r<5^her chapters may^ 
Isadvised to consult the Wa 
"this page for the current classificatioi^ 


Manuscript and illustrations for this volume were prepared for 
publication by the Summary Reports Group of the Columbia 
University Division of War Research under contract OEMsr-1131 
with the Office of Scientific Research and Development. This vol- 
ume was printed and bound by the Columbia University Press. 


Distribution of the Summary Technical Report of NDRC has been 
made by the War and Navy Departments. Inquiries concerning the 
availability and distribution of the Summary Technical Report 
volumes and microfilmed and other reference material should be 
addressed to the War Department Library, Room lA-522, The 
Pentagon, Washington 25, D. C., or to the Office of Naval Research, 
Navy Department, Attention: Reports and Documents Section, 
Washington 25, D. C. 


By 


-££ CLASSTFT7?n 
authority Secretary of 


I 

Jpopy No. 

263 


OCI lhi96o 

i^efense volume, like the seventy others of the Summary Technical 

Af^NiDRfg^^as been written, edited, and printed under 
Inevitably there are errors which have slipped past 
Division reaaay^SiS proofreaders. There may be errors of fact not 
known at time of printing. The author has not been able to follow 
through his writing to tfie final page proof. 

Please report errors to : 


JOINT RESEARCH AND DEVELOPMENT BOARD 
PROGRAMS DIVISION (STR ERRATA) 

• WASHINGTON 25, D. C. 


A master errata sheet will be compiled from these reports and sent 
to recipients of the volume. Your help will make this book more 
useful to other readers and will be of great value in preparing any 
revisions. 


LC REGULATION: BEFORE SERVICING 
OR REPRODUCING AN'^ PART OF THIS 
DOCUMENT, ALI. 0,-iASSIFIC ATION 

markings must be cancelled. 


S.UMMARY TECHNICAL REPORT OF DIVISION 6, NDRC 


VOLUME 20 


FLUID DYNAMICS 

TiT'.r.TASSlFIED. 

By authority Secretary of 

OCT ly I960 

Defense memo 2 August 1960 

library of congress 

1 I 

OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT 
VANNEVAR BUSH, DIRECTOR 

NATIONAL DEFENSE RESEARCH COMMITTEE 
JAMES B. CONANT, CHAIRMAN 


DIVISION 6 
JOHN T. TATE, CHIEF 


N 1. AjiniEiT 

JN sjVicmioE 


WASHINGTON, D. C., 1946 


NATIONAL DEFENSE RESEARCH COMMITTEE 


James B. Con ant, Chairman 
Richard C. Tolman, Vice Chairman 
Roger Adams ^ Army Representative^ 

Frank B. Jewett Navy Representative ^ 

Karl T. Compton Commissioner of Patents^ 

Irvin Stewart, Executive Secretary 


1 Army representatives in order of service: 

Maj. Gen. G. V, Strong Col. L. A. Denson 

Maj. Gen. R. C. Moore Col. P. R. Faymonville 

Maj. Gen. C. C. Williams Brig. Gen. E. A. Regnier 

Brig. Gen. W. A. Wood, Jr. Col. M. M. Irvine 

Col. E. A. Routheau 


2 Navy representatives in order of service: 

Rear Adm. H. G. Bowen Rear Adm. J. A. Purer 

Capt. Lybrand P. Smith Rear Adm. A. H. Van Keiiren 

Commodore H. A. Schade 
^ Commissioners of Patents in order of service: 
Conway P. Coe Casper W. Ooms 


NOTES ON THE ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee were 
(1) to recommend to the Director of OSRD suitable projects 
and research programs on the instrumentalities of warfare, 
together with contract facilities for carrying out these projects 
and programs, and (2) to administer the technical and scien- 
tific work of the contracts. More specifically, NDRC func- 
tioned by initiating research projects on requests from the 
Army or the Navy, or on requests from an allied government 
transmitted through the Liaison Office of OSRD, or on its own 
considered initiative as a result of the experience of its mem- 
bers. Proposals prepared by the Division, Panel, or Committee 
for research contracts for performance of the work involved in 
such projects were first reviewed by NDRC, and if approved, 
recommended to the Director of OSRD. Upon approval of a 
proposal by the Director, a contract permitting maximum 
flexibility of scientific effort was arranged. The business aspects 
of the contract, including such matters as materials, clearances, 
vouchers, patents, priorities, legal matters, and administration 
of patent matters were handled by the Executive Secretary 
of OSRI3. 

Originally NDRC administered its work through five divi- 
sions, each headed by one of the NDRC members. These were: 
Division A — Armor and Ordnance 
Division B — Bombs, Fuels, Gases, & Chemical Problems 
Division C — Communication and Transportation 
Division D — Detection, Controls, and Instruments 
I^ivision E — Patents and Inventions 


In a reorganization in the fall of 1942, twenty-three admin- 
istrative divisions, panels, or committees were created, each 
with a chief selected on the basis of his outstanding work in 
the particular field. The NDRC members then became a re- 
viewing and advisory group to the Director of OSRD. The 
final organization was as follows: 

Division 1 — Ballistic Research 

Division 2 — Effects of Impact and Explosion 

Division 3 — Rocket Ordnance 

Division 4 — Ordnance Accessories 

Division 5 — New Missiles 

Division 6 — Sub-Surface Warfare 

Division 7 — Fire Control 

Division 8 — Explosives 

Division 9 — Chemistry 

Division 10 — Absorbents and Aerosols 

Division 11 — Chemical Engineering 

Division 12 — Transportation 

Division 13 — Electrical Communication 

Division 14 — Radar 

Division 15 — Radio Coordination 

Division 16 — Optics and Camouflage 

Division 17 — Physics 

Division 18 — War Metallurgy 

Division 19 — Miscellaneous 

Applied Mathematics Panel 

Applied Psychology Panel 

Committee on Propagation 

Tropical Deterioration Administrative Committee 


Library of Congress 



490959 


NDRC FOREWORD 


AS EVENTS of the years preceding 1940 revealed 
more and more clearly the seriousness of the 
world situation/ many scientists in this country came 
to realize the need of organizing scientific research 
for service in a national emergency. Recommenda- 
tions which they made to the White House were 
given careful and sympathetic attention, and as a 
result the National Defense Research Committee 
[NDRC] was formed by Executive Order of the 
President in the summer of 1940. The members of 
NDRC, appointed by the President, were instructed 
to supplement the work of the Army and the Navy in 
the development of the instrumentalities of war. A 
year later, upon the establishment of the Office of 
Scientific Research and Development [OSRD], 
NDRC became one of its units. 

The Summary Technical Report of NDR(!l is a 
conscientious effort on the part of NDRC to Sum- 
marize and evaluate its work and to present it in a 
useful and permanent form. It comprises some 
seventy volumes broken into groups corresponding to 
the NDRC Divisions, Panels, and Committees. 

The Summary Technical Report of each Division, 
Panel, or Committee is an integral survey of the work 
of that group. The first volume of each group’s report 
contains a summary of the report, stating the prob- 
lems presented and the philosophy of attacking them 
and summarizing the results of the research, develop- 
ment, and training activities undertaken. Some v(|[- 
umes may be “state of the art” treatises covering 
subjects to which various research groups have con- 
tributed information. Others may contain descrip- 
tions of devices developed in the laboratories. A 
master index of all these divisional, panel, and com- 
mittee reports which together constitute the Sum- 
mary Technical Report of NDRC is contained in a 
separate volume, which also includes the index of a 
microfilm record of pertinent technical laboratory 
reports and reference material. 

Some of the NDRC-sponsored researches which 
had been declassified by the end of 1945 were of 
sufficient popular interest that it was found desirable 
to report them in the form of monographs, such as 
the series on radar by Division 14 and the monograph 
on sampling inspection by the Applied Mathematics 
Panel. Since the material treated in them is not dupli- 
cated in the Summary Technical Report of NDRC, 


the monographs are an important part of the story of 
these aspects of NDRC research. 

In contrast to the information on radar, which is 
of widespread interest and much of which is released 
to the public, the research on subsurface warfare is 
largely classified and is of general interest to a more 
restricted group. As a consequence, the report of 
Division 6 is found almost entirely in its Summary 
Technical Report, which runs to over twenty vol- 
umes. The extent of the work of a Division cannot 
therefore be judged solely by the number of volumes 
devoted to it in the Summary Technical Report of 
NDRC: account must be taken of the monographs 
and available reports published elsewhere. 

Any great cooperative endeavonpust stand or fall 
with the will and integrity of the men engaged in it. 
This fact held true for NDRC fronilts inception, and 
for Division 6 under the leadership of Dr. John T. 
Tat^^'^^gggfp^i^Did the men who worked with 
him- — Bombay nlemS^^fogivision 6, some as repre- 
XMvision’s contractors — belongs the 
sincere gratitude of the Nation for a difficult and 
often Q^JerliM ^ofeUvvell done. Their efforts con- 
tributed significantly to the outcome of our naval 
ODeratiog^g^\y;-i0gi^iiligui^rl%Sft richly deserved the 
■M^arm respoiise-4hi^ ^ceiy^d from the Navy. In 
J^^ft^i^^^^ccfimbutions to thcki knowledge of 
the ocean and to the art of oceanogmphic research 
will assuredly speed peacetime infestigations in 
this field and bring rich benefits to all mankind. 

The Summary Technical Report of Division 6, pre- 
pared under the direction of the Division Chief and 
authorized by him for publication, not only presents 
the methods and results of widely varied research 
and development programs but is essentially a record 
of the unstinted loyal cooperation of able men linked 
in a common effort to contribute to the defense of 
their Nation. To them all we exteock-^^^x^^^ 

OF THIS 

fjg" rKPRODUCHn ^ , ^ggxFlCA^O^ 

iscai'dh and Development 


J. B. CoNANT, Chairman 
National Defense Research Committee 




:f* * 







I ^ 


Ip 1*^. V ^ . 



^ *1' 







P-*" .; 4 / • 



|Xv‘>'v , 




1 


' 'i -J.'j "W** ’ 

. M V.^asrS ;3 

^ ^ ^ ■ ■ - 




f ’'i* s ‘ ►' ' ■■ j 

•,ij'*'i...- ?-•■-' 






► ^ 


.TW 




AT- 


• • 


^ -i 


\ ft 





»• /,; 


. ♦ K 





t'K;. •■•' 

L?.V .# V . 


> . f 


f i .ft. 


» ^ 


-r 






*t: 




u •* 


^.1 


‘ r * 

** k ■ V?» / 


i 


K’', pa(f:.’t , 




f^- 7 







’v?J 


rf-^ • ^ i* 


.■'0' n 

r • ^ ' •yM 


-.it 


I 


*r i 


i f . *f , •» * . ^ . 

1 ■♦ . N * ^ » • 



3 


4'' fi 


^fe.’;'t(^’'- i- 

►^v^s,,.:. ', 






IK> 


‘ *2? ; * 



r- 




PyV,*' . V >'. ■ '^'*4* ■ 

* , ^ * • ’ ' • ' 





? ^V'.' 



k'y 


•* V 


Kt*- jN 

^ O ' vi-. 


:S: 






1^: >r , 





'P i 


i t 


' .V. 

■ ■■ •V’-*"' *r. V 


r •.ii7*.‘i--k':ff**^J • ‘Hi '■‘' 


■Ji'tr 


'» I-*! 


'•SS^' . -.. 

f»--i L ^ , /V ‘ r? * 


• y* ‘i *. V* ■ 

' 











MAifl 1. 


r\ 





•- ‘ .s . 


.‘f • ^ 


* - '* y,-L-trJ^',i • 

T ->yv ” ■ .f® . -'ir' 















^ ^ Moa^ 




'■:> 


^vV* 


I- W e-*^! 

•; -M i - .’ 


'* ■■ *-n^ ^ / • 

4 .rf v^"* 

',* . -v-.^S - ■ '■■ * ^ 

‘ ' * 2 :, -1 




■ .:•■* 




4!^ 


r* r..*, 


' ■ .• -k Hl . > 


» ^ 


I • 


' 0 ilf - • 

Lujli ^ifr I 



FOREWORD 


S HORTLY AFTER SectioH C-4, later Division 6, was 
organized, the development of certain projectiles 
was undertaken. It soon became clear that additional 
data were required about how certain features of pro- 
jectile design, such as shape, weight distribution, 
etc., affect projectile travel in the air, behavior dur- 
ing the water-entry period and subsequent travel in 
the water toward the target. It is generally true that 
a projectile should be designed to secure both accurate 
travel to the target and efficient utilization of the 
applied propulsive forces. Whether these objectives 
are met in a particular design depends in part upon 
performance determined by the resultant effect of the 
aerodynamic and hydrodynamic, or, to employ one 
term, fluid dynamic force to which it is subjected in 
its travel. This report describes laboratory facilities 
developed and methods employed to establish defi- 
nite relationships between performance and design 
features, and the ffuid dynamic forces to which the 
projectile is subjected. Also, the report records the 
results of investigations on many projectile models, 
and, in addition, discusses quite fully certain cavita- 
tion phenomena observed. 

Following early studies, the Division in 1941 con- 
tracted with the California Institute of Technology 
to provide additional facilities in that Institution’s 
Hydrodynamics Laboratory and to conduct tests 


pertinent to the above objective. The facilities of the 
Hydrodynamics Laboratory were gradually expanded 
and methods for studying the dynamic behavior of 
projectiles were further developed. In addition to 
studies and tests upon projectiles being developed by 
Division 6, the laboratory was also able to undertake 
tests and supply data to other agencies also carrying- 
on the development of projectiles. 

The general project reported upon was under the 
direction of Dr. Robert T. Knapp to whom, together 
with his associate, Mr. Dailey, the Division is obli- 
gated for the preparation of this very complete re- 
port. The Division is also very appreciative of the 
fact that the Navy permitted the authors to complete 
this report after transfer of the project from Division 
to Navy support and direction. 

The Division feels that while this report describes 
the work undertaken primarily for the use of the 
Armed Services, it also contains material of interest 
and value to civilian science and technology and it is 
hoped that steps can be taken to declassify substan- 
tial portions of the information presented. 


John T. Tate 
Chief, Division 6 



vii 


I ' SjU * ‘ ■ ' <! 

X\ffr MM.^ '« >. 











fc- v>iMC 



^'4'f ' 


’v 


-Y 

' -r ' * .* ■• j/ . 

«-" . . ‘ • 'N 



vWVf.'V:^ « 

A- ;*.wfi. ';— 

st'V^»'^v JBI 

Ail U^xIm' t * ""^ » •■• * "S* H 


■ f i.ir. 'i— » ■ 

k’ »*.*./ ’'V‘a 


. * Ai 


-■ 


.'•• ' ' '.T, 

‘ ■ V'?f 


t ./. 






;'».: V-.,-, , .* 

f 3 r f, j,-. X t'’ * ■ * 


I *, 


* r 


-Y.< • ^.' ' 

' ' ,1 ‘ I ‘ * .* 





■? :e: '; 

# 



^vi.V'.j/^i . 





V# 



4 '■ i 
*.«.<# ■ 


I 








mh.M:^., 


<f. '•* _ I'^i' , , ' lijliil, 1 ■* ‘ 

• . ■ ' <■.•; i,“- ii'JfeK . 

C->, .■■;;•■ 

.A. ^ ■ '• ' ■*■'*., -; ' 


' 1 . 


"f . ;.'*4 

' .-.■^ ' ••..” 7 ;> ■ y*; i 

’ iS? #!••■ >.»*•.- ■ -|■•'■, >4 .)■’1L^ '“filj 



PREFACE 


T his volume presents the results of the work of the 
Hydrodynamics Laboratory of the California Insti- 
tute of Technology as part of the War Research Pro- 
gram from the fall of 1941 to the fall of 1945. The 
initial object of this work was to study the broad 
hydrodynamic aspects of the antisubmarine program. 
Later it was generalized to include the observation 
and an alysis of the hydrodynamic forces of bodies mov- 
ing through fluids and the development of satisfac- 
tory shapes for such bodies. These objectives and the 
development of the project are described in the first 
chapter. 

The bulk of the work during this war period neces- 
sarily and properly pertained to specific projectiles. 
Little time was available for research along basic 
lines. When feasible more generalized data were ob- 
tained and presented. In spite of concentration upon 
specific projects, by the end of the contract their 
number and diversity had provided an immense 
amount of data suitable for much additional general- 
ization. In preparing this volume, an attempt was 
made to organize and analyze this mass of data with 
the objective of ascertaining the basic factors in- 
volved. This was a lengthy process which required 
more time than was available during the closing 
weeks of the NDRC contract under which this proj- 
ect operated. Fortunately, however, the work of the 


project was continued under the auspices of the Navy 
Bureau of Ordnance, which organization generously 
permitted the laboratory to complete the preparation 
of the report. Thus it was possible to present the data 
in a much more general fashion than could have been 
done otherwise. This general information is basic to 
the design of nearly all projectiles and allied bodies 
and contributes to the understanding of the hydro- 
dynamic phenomena involved. Such information is of 
lasting value, not only to the problem of national 
defense, but to many other problems of industry and 
civilian technology. 

In closing these remarks, the author wishes to take 
this opportunity to express his appreciation to the 
staff of the Hydrodynamics Laboratory without whose 
loyalty and sincere effort this report could not have 
been possible. In thinking of the staff of a research 
laboratory, one is apt to include only the highly 
trained technical personnel and to omit others who 
contribute very important and vital skills and efforts. 
This is not the writer’s intention since he feels that all 
personnel made significant contributions which are 
hereby acknowledged. 

Robert T. Knapp 
Editor 


l2:aNFiiir:N'i'i vT 


IX 





CONTENTS 


CHAPTER PAGE 

1 Development of the Laboratory 1 

2 Laboratory Facilities 7 

3 Effect of Projectile Components bn the Flow 

Diagram 69 

4 Cavitation and Entrance Bubbles 96 

5 Nose Cavitation — Ogives and Spherogives . . 118 

6 Hydrodynamic Forces Resulting from Cavitation 

on Underwater Bodies 134 

7 Cavitation Noise from Underwater Projectiles . 155 

8 Forces on Finless Body Shapes 171 

9 Stabilizing Surfaces on Nonrotating Projectiles . 175 

10 Effects of Projectile Components on Drag, Cross 

Force, and Lift 185 

11 Effect of Projectile Components on Damping and 

Dynamic Stability 193 

12 Effect of Experimental Variables on an Air- 

Launched Projectile Trajectory 201 

13 Torpedoes 203 

14 Rockets and other Nonrotating Projectiles with 

Stabilizing Surfaces 230 

15 Spin-Stabilized Rockets 239 

16 Depth Charges 245 

17 Air Bombs 253 

18 Two-Dimensional Bodies 259 

19 Miscellaneous Investigations 271 

Appendix 275 

Glossary 281 

Bibliography 283 

Contract Numbers 286 

Project Numbers 287 

Index 289 




Chapter 1 


DEVELOPMENT OF THE LABORATORY 


PURPOSE AND HISTORY OF THE 
‘ LABORATORY 

^ ^ ^ Laboratory Objectives 

D uring the four-year period from the fall of 
1941 to the fall of 1945, the Hydrodynamics 
Laboratory of the California Institute of Technolog}^ 
[CIT] devoted its entire resources to the prosecution 
of a war research program for the Office of Scientific 
Research and Development [OSRD] under the direc- 
tion of Division 6 of the National Defense Research 
Committee [NDRC]. The general assignment was to 
observe and analyze the hydrodynamic forces acting 
on bodies moving through fluid media, and to de- 
velop shapes for these bodies that would result in the 
specific performance characteristics desired. With 
very few exceptions, the bodies studied were pro- 
jectiles. The larger part of the time and energy avail- 
able was used in studying the behavior of projectiles 
whose trajectories were either partly or wholly un- 
der water. However, a very significant part of the 
laboratory activities was given over to work on air- 
flight projectiles operating at velocities enough lower 
than the velocity of sound so that the air could be 
considered incompressible. Much consideration was 
also given to the water entry problems associated 
\\Tth air-launched underwater projectiles such as 
aircraft torpedoes and antisubmarine rockets. 

^ ^ Historical Development of the 
Project 

The need for this project developed in the New 
London Laboratory of the Columbia University 
Division of War Research [CUDWR-NLLJ. The ini- 
tial task of this laboratory was to study the broad 
aspects of the antisubmarine program. In June 1941, 
Robert T. Knapp, a member of the CIT Mechanical 
Engineering Department, was requested to act as a 
consultant of the New London Laboratory on various 
hydrodynamic aspects of their research program. 

Later in the summer the New London Laboratory 
became interested in the development of a stream- 
lined depth charge which would have a much higher 
fall velocity in sea water than that of the Ashcan, the 
surface ship depth charge in use at that time. One of 


the several disadvantages of the Ashcan was that its 
fall velocity was so low and its trajectory so erratic 
that the probability of securing a hit on a moving 
submarine operating at or below medium depth was 
very low. It was felt that a barrage of smaller, fast- 
sinking charges would have a much higher probability 
of securing a hit. Soon after the development of the 
high-velocity streamlined charge was begun, it be- 
came evident that serious problems concerning its 
stability and the prediction of its trajectory must be 
overcome if a satisfactory weapon was to be obtained. 
This meant that it would be necessary to determine 
the hydrodynamic characteristics of the various 
shapes proposed for the new charge. 

Consideration was first given to use of a wind tun- 
nel for such a study. However, it was soon found that 
existing wind tunnels were all heavily loaded with 
aerodynamic problems for the Army, Navy, and 
various manufacturers, and that it would be impossi- 
ble to obtain results for as long a period and as 
rapidly as would be required. Furthermore, it was 
felt that there were some important phenomena such 
as cavitation that were peculiar to water and liquids 
in general and that would undoubtedly affect the 
performance of the projectile. This class of phenom- 
ena could not be studied directly in a wind tunnel. 
Therefore, in August 1941, the construction of a 
small water tunnel for the purpose of studying the 
underwater behavior of projectiles was proposed and 
approved. The project was undertaken by the Hy- 
draulic Machinery Laboratory [CIT-HML] because 
much of the basic equipment of that laboratory could 
be adapted to the use of the water tunnel, and thus a 
working tool could be obtained more economically 
and in a much shorter time than if the project had to 
be built from the ground up. 

A staff was immediately organized, which included 
a group to design the special apparatus and instru- 
ments needed, and the tunnel was put into operation 
early in the spring of 1942. It remained in continuous 
operation from that time to the termination of the 
contract in September 1945. 

The same need for information that resulted in the 
sponsorship of the water tunnel was also responsible 
for the initiation of another small project — the de- 
sign and construction of a polarized light flume. The 


c ferUlTr^ HI '1 


1 


2 


DEVELOPMENT OF THE LABORATORY 


purpose of this development was to furnish a tool for 
use in studying the flow pattern around underwater 
projectiles. Recent work in the Chemical Engineering 
Laboratory of the Massachusetts Institute of Tech- 
nology had demonstrated that dilute suspensions of 
certain varieties of bentonite exhibited the property 
of streaming double refraction to such a marked de- 
gree that they could be used to make flow visible. 
Permission was therefore requested and obtained 
from Davis R. Dewey II for the use of this develop- 
ment for the study of flow patterns. 

Since the tunnel, and especially its associated 
equipment, had to be constructed with very little 
precedent, it underwent a continuous development 
during the entire time. For example, in the beginning 
the order of accuracy of the force measurements was 
relatively low but it was adequate to give the infor- 
mation required for the problems that presented 
themselves. The accuracy of the laboratory improved 
rapidly with experience and was able to keep pace 
with the needs of the program. 

The first projectile that was studied in the tunnel 
was the streamlined depth charge that was responsi- 
ble for its initiation. Before the work on this projectile 
was completed, a demand arose for the development 
of an instrument case to house some delicate equip- 
ment to be towed by a cable from an airplane. To 
secure satisfactory operation of these instruments it 
was necessary that this case should have a low drag, 
should be very stable, and should have slow responses 
to disturbing gusts in the air. 

Early in the life of the laboratory a close liaison 
was set up and continuously maintained with the 
rocket program being carried out for NDRC Division 
3 by CIT under Contract OEMsr-418. 

The first group of rockets to be studied were of the 
Mousetrap type of depth charge which were in the 
same general class as the small streamlined depth 
charges being developed by CUDWR-NLL. Later 
many other types of rockets were tested for Division 
3, some of which were designed to have the final part 
of their trajectory under water, but most of which 
were regular air-flight rockets for general use against 
land or surface targets. 

In the winter of 1942-1943 the laboratory assign- 
ment was expanded to include the first of a series of 
projectiles from Army Ordnance through requests 
originating at the Ballistic Research Laboratory at 
Aberdeen Proving Ground, Maryland. Included in 
this series was the bazooka. In the initial models this 
rocket had shown evidence of having insufficient sta- 


bility in flight. A rather extensive program of tests 
resulted in the development of a series of stabiliz- 
ing surfaces, generally of the ring-tail type, which 
improved the accuracy and reliability of the de- 
vice. 

Another rocket studied was the 4.5-in. which was 
equipped with folding fins. Investigations were also 
carried out for the same organization with a view to 
improving the stability of small mortar projectiles. 

During 1942 the laboratory also made an investi- 
gation on the first of a long series of torpedoes of all 
types. The torpedo was the first projectile to be 
studied which had movable fins controlled by a steer- 
ing mechanism. This required a much more elaborate 
series of tests and demanded higher accuracy than 
the rest of the program. In the latter half of 1943 the 
aircraft torpedo became a major part of the labora- 
tory’s activities. 

The first problem to be presented concerned the 
stability of the Mark 13 torpedo and its behavior dur- 
ing water entry. The ensuing study resulted in the 
suggestion that the “ring tail” be added to the exist- 
ing stabilizing fin structure. After a rapid but thor- 
ough series of full-scale laboratory and field tests, 
this suggestion was adopted. Torpedoes so equipped 
saw much field service before the close of the 
war. 

The problems involved in the performance of the 
aircraft torpedo included not only its performance 
characteristics in the steady running state, but also 
its behavior in air, the phenomenon of water entry, 
and the behavior while operating within the cavity 
formed when it enters the water. These phases of the 
operation before the torpedo reached its steady run- 
ning state involved phenomena which could not be 
studied adequately by the use of the water tunnel 
alone. Furthermore, by this time the original staff 
had increased tenfold, and the lack of suitable work- 
ing space was so acute that the effectiveness of the 
organization was severely impaired. 

The Office of Scientific Research and Develop- 
ment, therefore, authorized CIT to construct a new 
building and two additional pieces of major equip- 
ment for use of the project. The first item of new 
equipment was a variable-pressure launching tank 
designed for the purpose of studying the entry phase 
of the aircraft torpedo trajectory. The second item 
was a free-surface water tunnel for use in investigat- 
ing shallow-water running operation within the 
cavity and the problems involved in underwater jet 
propulsion. The building was designed as a wing ad- 


rrTMtJTrFNTf Af 


LABORATORY CAPABILITIES AND LIMITATIONS 


3 


joining the Hydraulic Machinery Laboratory, which 
made it possible to unify the laboratory and office 
work. Construction of the building was commenced 
in July 1944, and it was occupied in December of the 
same year. Design and construction of the equipment 
was started simultaneously with that of the building. 
The launching tank was completed and preliminary 
measurements were made in the spring of 1945. This 
development was continued up to the close of the 
contract. The construction of the free surface water 
tunnel proceeded more slowly due to the fact that top 
priority had been assigned to the launching tank. The 
major parts of the equipment were completed and 
assembly was started in the laboratory during the 
final month of the contract. 

12 LABORATORY CAPABILITIES 
AND LIMITATIONS 

One method of analyzing the capabilities and 
limitations of the laboratory consists in comparing 
the facilities with the details of the field of study 
assigned to it. This requires a specific statement of 
the problem. It may be outlined as follows: The main 
field of investigation of the laboratory has been the 
study of the interactions between air- or water- 
launched underwater projectiles and the media 
through which they travel, as these interactions af- 
fect the trajectory and the other external performance 
characteristics of the projectile. This study has been 
limited to the use of small-scale projectiles in the 
laboratory. Confirmation checks on full-scale pro- 
jectiles have been carried out by other agencies. No 
studies have been undertaken in this laboratory con- 
cerning the mechanical strength of the projectiles, 
their internal construction, power plants, or explosive 
charges. In other words, the studies have been 
purely aero- and hydrodynamic in character. 

1 2.1 Hydrodynamic Problems of 
Underwater Projectiles 

In order to analyze the subdivisions of the work 
more closely it will be profitable to examine the 
trajectory of a typical projectile to see what problems 
present themselves along the path. The most versa- 
tile projectile studied by the laboratory has been the 
aircraft torpedo. It also presents the greatest number 
of problems. Therefore, the examination of the parts 
of its trajectory from the time it leaves the aircraft 
until it hits the selected target will serve to bring 


out the general problems encountered by the labora- 
tory. 

The trajectory of the aircraft torpedo may be 
subdivided into four parts: 

1. The air flight from the plane to the water 
surface. 

2. Passage through the air-water interface and 
subsequent motion within the cavity formed during 
this passage. 

3. The underwater run after the torpedo leaves the 
cavity. 

4. The period of terminal ballistics beginning when 
the projectile hits the target. 

A diagram of the trajectory showing these subdivi- 
sions will be seen in Figure 1. 

The hydrodynamic problems involved in parts 1, 
2, and 3 nearly all center around the external forces 
acting on the projectile and its resulting motion. 
Parts 1 and 3 have much in common since they are 
both concerned with the motion of the projectile in a 
homogeneous fluid. The differences that do exist can 
be traced to the great differences in density of the 
fluids involved, that is, air in part 1 and sea water in 
part 3. Satisfactory stability and damping character- 
istics are necessary for both parts of the trajectory. 
However, these characteristics differ widely for the 
two parts because, while the mass of the projectile 
remains constant, the external forces differ greatly in 
magnitude, although not in kind, due to this dif- 
ference in fluid density. The problems peculiar to 
part 2 involve transient force systems rather than 
steady ones. Furthermore, the forces differ widely in 
magnitude, direction, and point of application from 
those existing either in parts 1 or 3. During part 2 the 
projectile no longer moves through a homogeneous 
fluid, but is acted on by both the air and the water. 
This results from the fact that a cavity is formed in 
the water during the passage of the projectile through 
the interface. This cavity is filled with air and persists 
for a considerable distance along the underwater 
trajectory. During part 3 the drag or resistance to 
forward motion becomes of more importance than in 
the preceding parts of the trajectory, because here it 
is the determining factor of the underwater speed and 
range of the projectile. Another problem arises in 
connection with part 3. Considerable noise may be 
produced by the projectile as it moves through the 
water. Although this noise does not affect the hydro- 
dynamic operation of the torpedo, it may be unde- 
sirable for other reasons and hence presents a problem 
for study and elimination. In part 4 the hydrody- 


4 


DEVELOPMENT OF THE LABORATORY 



namic problems no longer involve the forces and 
motions of the projectile, but are concerned with the 
forces resulting from underwater explosions. 

^ ^ ^ Methods of Study 

Available in the Laboratory 

The general method of attack used by the labora- 
tory in studying projectile characteristics is the isola- 
tion and measurement of the individual properties 
one by one under controlled conditions with a view to 
obtaining the information necessary to understand 
the overall performance. The alternate method of 
attack is to observe the overall trajectory in order to 
determine the resultant forces by analyzing the cor- 
responding motions at different instants along the 
path. When adequate facilities are available, the two 
methods can be worked together to good advantage, 
the one contributing to the other. 

All of the work in this laboratory was carried on by 
the use of models, most of which were constructed to 
the standard diameter of 2 in. The main reason for 
using small models instead of full-scale projectiles is 
that the models require much less time to construct 
and test and, therefore, are peculiarly adapted to the 
pressure of a wartime research program. In addition, 
research with models is much less expensive, not only 
because the models themselves are much cheaper to 
construct, but also because the basic testing equip- 
ment costs only a small fraction of what it would for 
full-size tests. Another very appreciable advantage 
which is especially important in wartime is that the 
small-scale work requires a much smaller staff of 
trained personnel to achieve the same results. It 
should be noted that the word “modeh’ by no means 
implies that the studies are restricted to empirical 


investigation of specific projectiles. They can, of 
course, be used for all types of basic investigations as 
well. In fact, when basic investigations are consid- 
ered, the terms “modeP’ and “model scale” lose their 
significance. 

The laboratory has available four major pieces of 
equipment. They will be described in some detail in 
the following chapter. However, a comparison of the 
general type of work for which they are suitable with 
the problems involved in the four subdivisions of the 
typical trajectory described in the preceding section 
will serve to show the capabilities and limitations 
of the laboratory in handling the problems as- 
signed. 

Figure 2 shows the typical trajectory of an air- 
launched underwater projectile. On it are superim- 
posed symbols representing the four major pieces of 
equipment of the laboratory together with arrows 
indicating the fields of study for which each is 
adaptable. 

High-Speed Water Tunnel 

This is the most versatile piece of equipment in the 
laboratory and the one that has been in operation for 
the duration of the project. It was designed primarily 
for the measurement of the forces and moments act- 
ing on projectile shapes. As a result of various modi- 
fications and developments, it has been found suit- 
able for the following types of measurements: 

1. Steady-state forces and moments. 

2. Damping forces. 

3. Inception and development of cavitation. 

4. Forces acting on cavitating bodies. 

5. Noise produced by cavitation. 

6. Powered model studies. 


:()\FfDF>m\ 


LABORATORY CAPABILITIES AND LIMITATIONS 


5 


7. The effect of exhaust gases on force and cavita- 
tion characteristics. 

Polarized Light Flume 

This is an auxiliary piece of equipment used 
principally to supplement the work of the high-speed 
water tunnel. Its chief characteristic is that it gives 
the visual picture of the flow around immersed bodies. 
These results are qualitative rather than quanti- 
tative. It has been employed chiefly for the following 
purposes: 

1. The determination of hydrodynamically unde- 
sirable features of existing or proposed projectiles as 
evidenced by the formation of bad eddies, zones of 
separation, etc. 

2. The design of stabilizing surfaces, especially 
ring tails, to set the flow pattern so as to reduce the 
resultant drag to a minimum. 

3. The study of the action of various components 
of projectiles as evidenced by their effect on the 
flow. 

Controlled-Atmosphere Launching Tank 

This was especially designed to study the problems 
associated with the entry of the projectile into the 
water from the air and those of the phase immediately 


following, in which the projectile is surrounded by 
the bubble that is formed during the entry. These 
problems differ in one important respect from those 
of the air flight and the steady-state underwater run in 
that in the two latter phases only one fluid is involved 
at a time, whereas in the entry and cavity phases, 
both the gas and the liquid are involved. It is for this 
reason that the launching tank is so arranged that the 
pressure can be varied at will. The use of this feature 
will be discussed more fully in Chapter 12. It is 
interesting to note that the final portion of the 
trajectory, i.e., the terminal ballistics, also involves 
phenomena in which the interactions of the gas and 
liquid phases are important. The underwater explo- 
sion produces a large volume of gas. The damage 
produced by underwater explosions is largely con- 
trolled by the behavior of this gas and its interaction 
with the hydrodynamic forces. The facilities em- 
bodied in the launching tank are adapted with little 
or no modification to a small-scale study of under- 
water explosions. 

Free-Surface Water Tunnel 

This is the fourth and latest major piece of equip- 
ment of the laboratory. Its basic features are very 
similar to those of the high-speed water tunnel since 
it offers a working section in which bodies may be 



Figure 2. Application of laboratory equipment to study of torpedo behavior. 


6 


DEVELOPMENT OF THE LABORATORY 


supported in a stream of flowing water so that meas- 
urements can be made of the force and other hydro- 
dynamic characteristics. It has the unique feature, 
however, that the upper surface of the working sec- 
tion is not a solid boundary, but is a free surface, i.e., 
an air-water interface. The pressure at this interface 
may be maintained at any desired value from at- 
mospheric down to about V15 of an atmosphere. This 
makes it possible to study problems which cannot be 
dealt with effectively in the high-speed water tunnel. 
For example, if torpedoes of a certain design ap- 
proach too close to the surface, they will broach and 
then run on the surface since the controls are inade- 
quate to make them submerge again. These controls, 
however, appear quite adequate for the normal 
underwater run. This shows that the hydrodynamic 
forces acting on the body when it is near the surface 
are different from those acting during deep running. 
These forces and their variation with distance to the 
surface can be studied effectively in the free-surface 
water tunnel. 

One of the unanswered questions involved in the 
use of jet propulsion in underwater projectiles is the 
effect of the jet on the resistance and the control 
characteristics of the projectile. The experimental 


study of this effect requires the introduction of 
relatively large amounts of air or other gas into the 
working section in order to form a jet with the desired 
characteristics. Such a study cannot be undertaken 
in the high-speed water tunnel because it is not equip- 
ped to remove this large amount of gas after it leaves 
the working section. If it is not removed, it circulates 
with the water and in a very few seconds is back to 
the working section again. This is not permissible be- 
cause it affects all the hydrodynamic forces and in- 
validates the measurements. The free-surface water 
tunnel, therefore, was designed with a high-capacity 
air-removal system to make it adaptable to detailed 
study of the effects of underwater jets. 

The controlled-atmosphere launching tank was de- 
signed to give information concerning the overall be- 
havior of the projectile during its passage through the 
interface and its run in the bubble. However, it was 
felt that it would be very helpful to be able to make 
force measurements and to observe cavity character- 
istics under steady-state conditions. This will be 
possible with the free-surface water tunnel since pro- 
jectiles can be mounted on a balance above the water 
surface and the forces on them can be measured for 
any degree of submersion. 



Chapter 2 

LABORATORY FACILITIES 


2 1 PHYSICAL ARRANGEMENT 
OF LABORATORY 

T he laboratory facilities of the project are 
housed in the new Hydrodynamics Laboratory 
building and in the adjoining Hydraulic Machinery 
Laboratory. The Hydrodynamics Laboratory, which 
is shown in Figure 1, occupies three floors. Labora- 
tory equipment is located on the basement and sub- 
basement floors, with offices on the ground floor. The 
Hydraulic Machinery Laboratory occupies four sto- 
ries in the left-hand wing of the Guggenheim Aero- 
nautics Laboratory building which appears in the 
background in Figure 1 . The buildings are intercon- 
necting on all three floors of the Hydrodynamics 
Laboratory. 



Figure 1. Hydrodynamics Laboratory building. 

Figures 2A, B, and C show the three floor plans 
and arrangement of major equipment and auxiliary 
facilities in both buildings. The total floor space 
available is approximately 19,000 sq ft. The high- 
speed water tunnel equipment occupies all four sto- 
ries of the Hydraulic Machinery Laboratory area 
sho\\Ti on the left in Figure 2. The working section 
and main operating level is on the first floor with 
circulating pump, water storage, and miscellaneous 
auxiliary equipment on the floors below. There is no 
floor at the second-floor level; the space is used for 
additional head room over the water tunnel. The con- 
trolled-atmosphere launching tank and the free-sur- 
face water tunnel, together with their storage tanks 
and auxiliaries, occupy two floor levels (basement and 
subbasement) in the adjoining new building. The 
polarized light flume is on the basement level. 


It will be noted that in addition to the primary 
apparatus, space is provided for all the activities of 
the project auxiliary to the main experimental work. 
The first floor of the new Hydrodynamics Laboratory 
provides for administrative offices, design offices, and 
drafting rooms, computing rooms for reduction of 
experimental data, and quarters for analysis of re- 
sults and preparation of technical reports. The base- 
ment floor contains photographic laboratories. The 
subbasement houses a machine shop for construction 
of test models. The electronics laboratory and shop 
are located adjacent to the water tunnel on the base- 
ment level. 


2 2 HIGH-SPEED WATER TUNNEL 

2.2.1 Purpose and Specifications 

The high-speed water tunnel was designed and 
constructed to permit the determination of the hy- 
drodynamic forces on projectiles when in the airborne 
or waterborne phases of the trajectory. The design 
of the apparatus is based on the relative -flow principle 
employed in wind tunnels wherein the flow pattern 
peculiar to the prototype moving through a station- 
ary fluid is simulated by the flow pattern about a 
model immersed in a moving fluid. The essential 
components of the tunnel are: 

1. A working section in which the model may be 
mounted and observed. 

2. A circulating system consisting basically of a 
pump and piping by which the flow of water may be 
maintained through the working section. 

3. A measuring system or balance by means of 
which the hydrodynamic forces on the model may be 
measured. 

A general view of the high-speed water tunnel is 
seen in Figure 3. The essential features mentioned 
above will be seen and identification of most of the 
other components can be made by reference to the 
isometric drawing. Figure 4, and to the elevation 
drawing. Figure 5. The relationship of the high-speed 
water tunnel to the other main pieces of apparatus 
in the Hydrodynamics Laboratory can be seen on the 
floor plan. Figure 2. 




7 


8 


LABORATORY FACILITIES 



Figure 2A. Hydrodynamics Laboratory, ground floor level. 

The construction of the tunnel centered around the 
existing equipment in the Hydraulic Machinery Lab- 
oratory. In addition to the general basic laboratory 
layout available for use, the following important 
components were available: 

1. The electric dynamometer. 

2. The dynamometer speed control system. 

3. Special weighing-type pressure gauges. 

4. The pressure control system. 

5. The temperature control system. 

6. The 60-in. diameter tank used as part of the 
main water tunnel circuit and for air-removal pur- 
poses. 

The existence of this equipment was very impor- 
tant as a time-saving factor in getting the laboratory 
into productive work. 

The specifications for the water tunnel were de- 
veloped around the capabilities of the above-men- 
tioned existing equipment and the needs of the Na- 
tional Defense Research Committee [NDRC]. An 



enumeration of the main specifications of the water 
tunnel follows . 

Velocity 

The lower limit of the acceptable maximum ve- 
locity was set at 50 fps since it was felt that existing 
developments showed a definite trend toward higher 
and higher velocities for Service applications. The 
available horsepower in the electric dynamometer 
has permitted maximum speeds of 75 fps. 

Dimensions of Working Section 

A closed-type working section was decided upon 
because such a design reduces the energy loss, gives 
more stable flow, and results in a more definite 
and calculable boundary correction to the measure- 
ments as compared with other types of working 
sections. 



HIGH-SPEED WATER TUNNEL 


9 


The acceptable model sizes and scales determine 
the size of the tunnel. It is axiomatic that models 
should be kept as small as compatible with desired 
accuracy and reliability of the test results, since 
smallness makes for economy, speed, and flexibility, 
and therefore increases the productivity of the labo- 
ratory. It was estimated that the prototype diameters 
of the bodies to be studied would vary from 2 to 24 in. 
Since the measurements were to be made in water, 
which is a fluid of high density and low viscosity, it 
was felt that a model diameter of 2 in. would result in 
forces of reasonable magnitude and at the same time 
the flow conditions would be comparable to service 
conditions. In other words, a 2-in. model tested 
in the high-speed tunnel gives sufficiently large 
Reynolds numbers to be comparable with prototype 
conditions. 

On this basis it was decided that the working sec- 
tion should be 14 in. in diameter. This is in accord- 
ance with current wind-tunnel practice for dirigibles 
and similar symmetrical bodies, i.e., to have a model 


diameter of about 15 per cent of that of the measur- 
ing section. 

Aerodynamic practice has shown that the test 
chamber should be considerably longer than the 
model if accurate drag measurements are to be ob- 
tained. The maximum prototype length was esti- 
mated to be 8 to 10 diameters, with average length 4 
to 6 diameters. This would make the average model 
length 8 to 12 in. with extremes to 20 in. For the 
NDRC work it was felt that a large working section 
would also permit more extensive observations of the 
wake. Therefore, a 72-in. working section was chosen. 

Balance Equipment for Force Measurements 

The choice of the type of balance is one of the most 
difficult problems in connection with the tunnel. The 
balance is a necessary evil. The forces on the body 
under study must be measured, but any connection 
to the body to provide means of measuring these 
forces changes the forces themselves and thus a cor- 



Figure 2B. Hydrodynamics Laboratory, basement level. 

C jjfinNFini.NTTAir ' J 


10 


LABORATORY FACILITIES 



Figure 2C. Hydrodynamics Laboratory, subbasement level. 


rection must be made. An analysis of the measure- 
ment desired shows that the balance system can be 
relatively simple, since the bodies to be studied have 
axial symmetry. A three-component balance, there- 
fore, is capable of furnishing all the necessary infor- 
mation since the possible forces acting on the body 
can be reduced to a drag force in the direction of flow, 
a cross force or lateral force, and a moment about an 
axis normal to the direction of flow. One additional 
factor entered into the selection of balance type. It 


was anticipated that it would be necessary to study 
the characteristics of propelled bodies, whether the 
force of propulsion came from a propeller or a jet of 
fluid. This precluded the use of a balance which at- 
taches axially to the rear of the body. The wire type 
of balance attachments was also eliminated because 
it provided no possibility for introducing a supply of 
fluid for the driving jet. Therefore, a single spindle- 
type balance was decided upon with the model axis 
normal to that of the spindle. 




HIGH-SPEED WATER TUNNEL 


11 


Requirements for Cavitation Studies 

If submerged bodies are required to travel at high 
speeds near the water surface, cavitation may result 
and produce serious deviations from the expected 
performance. In order to study the effects of cavita- 
tion in the model performance two additional re- 
quirements were introduced: (1) that the absolute 
pressure in the measuring section be variable without 
affecting the velocity of the flow, and (2) that pro- 
vision be made for visual observation of the location 
and the action of the cavitation when it was produced. 

2.2.2 Main Water Tunnel Circuit 
Flow Circuit 

The flow circuit can be traced in either Figure 4 or 
5 by starting with the circulating pump. This is 
driven by a dynamometer through a multiple V-belt 


drive having a speed reduction of 2 to 1. The pump 
discharges horizontally to the right through a diffuser 
section into the 5-ft diameter vertical tank. At this 
point, the flow is turned upward by vanes inside the 
tank and, at the working-section level, it is turned 
horizontally to the left by vanes into a short length of 
34j^-in. pipe. From there the flow passes through a 
honeycomb and a reducing nozzle to the 14-in. dia- 
meter working section. From the working section, the 
flow enters another horizontal diffuser which reduces 
its velocity considerably before entering the elbow. 
From the elbow the flow enters the diverging down- 
comer, which completes the deceleration before the 
flow reaches the inlet of the circulating pump. 

Circulating Pump and Drive 

Figure 6 is a view of the circulating pump taken 
from the discharge end. Figure 7 shows the pump 
from the driving end and Figure 8 is a view into the 


j; dm Kflucr-csiua 


an. 


rra nn 

tin 



i-n- ^ 

f 


i. r y 


■t 


JUT 

T”' ■ i T_ y"--T l»»~r 



#JJ • J- ^ 


t/ . ■ .■ 



L 




f ^ r" . . r 






- CM 








r 


'‘J])/ 

A m 




rliCM Speed 
Water, Tunnel 

HYDRODYNAMICS LATiORA FORY 

Caliibrnia Institute of Technology 


Figure 3. High-speed water tunnel. Hydrodynamics Laboratory, California Institute of Technology. 


12 


LABORATORY FACILITIES 




Figure 5. Elevation drawing. High-speed water 
tunnel. 


pump inlet showing the straightening vanes. The 
source of power for the circulating pump is the dyna- 
mometer shown in Figure 9. This is a direct-current 
machine with a rated continuous capacity of 275 hp 
and a speed range of 100 to 5,000 rpm. It is cradle 
mounted so that the horsepower for operating the 
tunnel may be measured readily. The dynamometer 
is coupled to the circulating pump through the V- 
belt drive shown in Figure 7. Twenty belts are used 


in multiple for this drive, which has a rated capacity 
of 250 hp. 


Speed Control 

It is essential that constant water velocity be 
maintained in the working section. This means that 



Figure 6. Circulating pump for high-speed water 
tunnel. View from discharge end. 


the circulating-pump speed and, hence, the dyna- 
mometer speed must be controlled very closely. The 
speed-control system employed is shown by the block 
diagram. Figure 10. 

The system is built around two synchronous mo- 
tors, one operated by the quartz-crystal controlled, 
standard-frequency system and the other by the 
alternator on the dynamometer shaft. These drive 
two shafts of a small bevel-gear differential. The third 



Figure 7. Circulating pump for high-speed water 
tunnel. View from driving end. 



HIGH-SPEED WATER TUNNEL 


13 


shaft, therefore, turns at a speed proportional to the 
difference of the other two. This shaft actuates a 
phase shifter (in this case a selsyn motor driven 
through a friction clutch and limited in motion by 



Figure 8. Circulating pump for high-speed water 
tunnel. View into pump inlet, showing the straighten- 
ing vanes. 

stops) which controls the output of a battery of 
thyratron rectifiers. These furnish the excitation 
field for the shunt- wound dynamometer, and thus 
control its speed. It will be seen that any difference in 
speed between the dynamometer and the speed 
standard acts immediately to correct itself. The only 
position of equilibrium is absolute synchronism of the 


two systems. The speed-control gear box is shown in 
Figure 1 1 . This control system permits a speed range 
for the dynamometer of from 100 to 5,000 rpm. 
For any given setting, the average speed is as ac- 



Figure 9. Dynamometer for circulating pump for 
high-speed water tunnel. View from above. 


curate as the quartz crystal controlling the standard- 
frequency source; about 1 part in 50,000. The in- 
stantaneous speed fluctuations are of the order of 
1 rpm. 



Figure 10. Block diagram of speed-control system for dynamometer, high-speed water tunnel. 

Ery)NFlDMNTl Al. y 






14 


LABORATORY FACILITIES 


Air Removal and Flow Straightening 

The 5-ft diameter tank, besides furnishing part of 
the primary flow circuit, provides a high point in the 
system for removal of accumulated air, as shown in 
Figure 12. The honeycomb is shown in detail in 



Figure 11, Speed control gear box for dynamometer, 
high-speed water tunnel. View from above. 


Figure 13 and its location in the circuit is shown in 
Figure 5. The honeycomb consists of a nest of axial 
channels 103 ^ in. long and of triangular cross section, 
1 in. on a side. This design is very easy to build out of 
light galvanized iron sheet and it has been a satis- 
factory means of removing the lateral-velocity com- 
ponents at the entrance to the nozzle. 

Nozzle 

The nozzle is shown before assembly in the circuit 
in Figure 14 and after assembly in Figure 15. It re- 


duces the flow cross section from 34%-in. diameter 
to the 14-in. diameter of the working section in a 
length of 47 in. The contour is designed to give a uni- 



Figure 12. Five-foot diameter tank, high-speed water 
tunnel. 


form velocity distribution across the flow at the en- 
trance to the working section with no lateral-velocity 
components. This rather elaborate design was found 
necessary in order to eliminate local cavitation in the 
nozzle when the tunnel was being operated with low 
pressure and high velocity in the working section. 
The nozzle is fabricated steel plate machined to the 
specified contour, cadmium plated, and polished on 
the inside surface. Figure 15 shows the piezometer 
rings used to measure the pressure drop across the 
nozzle from which the velocity of flow in the working 
section is computed. Between the nozzle and the 



HIGH-SPEED WATER TUNNEL 


15 


working section is seen the 23 /^-in. thick dummy pitot 
tube block. This can be removed and replaced with 
an identical block drilled for the direction-finding 
pitot tube when a velocity traverse of the flow is to be 
taken. 



Figure 13. Honeycomb baffle. High-speed water 
tunnel. 


Working Section 


which, in turn, is bolted to the nozzle. Locating 
dowels are used to insure proper alignment. Unsup- 
ported-area type neoprene gaskets are used to permit 
metal-to-metal contact of the flanges and to eliminate 
any possibility of gasket material projecting into the 
flow. The downstream end of the working section is 
connected to the diffuser by a Victaulic coupling. 



Figure 15. Nozzle after assembly. High-speed water 
tunnel. 


This eliminates any mechanical stress on the working 
section and provides for small misalignments and 
thermal expansion. 


The working section used during the latter part of 
the project is shown before assembly in Figure 16 and 
after assembly in Figure 17. The bulkheads and re- 
inforcing permit the use of the large Lucite windows 
for photographic purposes. The upstream end of the 
working section is bolted to the pitot tube block 



Figure 14. Nozzle before assembly. High-speed 
water tunnel. 


^ ^ ^ Auxiliary Circuits 

Pressure Regulating Circuits 

Several auxiliary circuits are used in connection 
with the main circuit to obtain the desired operating 
flexibility. The water tunnel operates on a closed cir- 
cuit in a completely filled sytem; therefore, it is 
possible to impose other minor flow circuits on this 
system without disturbing the main flow. This princi- 
ple is used to obtain pressure control of the system. 



Figure 16. Working section before assembly. Rear 
view. High-speed water tunnel. 









16 


LABORATORY FACILITIES 


The pressure-regulating circuit pump is submerged 
in an open storage tank. The discharge goes to the 
5-ft diameter tank through the horizontal pipe in 
Figure 5. Since the system is full, this same amount of 
water must leave the tank through the by-pass valve. 
The by-pass valve is motor-operated and is controlled 
from the working floor. The pressure in the 5-ft dia- 
meter tank varies with the amount of opening of 
this by-pass valve. When it is nearly closed, the 
tank pressure reached the maximum head which 
the pressure-regulating pump can develop, i.e., 
about 150 ft. Opening the by-pass valve reduces the 
head until atmospheric pressure is reached at that 
point. Since the working section is about 15 ft 
above the valve and since a large additional pressure 
drop is caused by the acceleration of the flow in the 
nozzle ahead of the working section, subatmospheric 
pressures can be obtained at the test station. How- 
ever, if still lower pressures are desired, a booster 
pump located in the by-pass line, but not shown 
in this drawing, may be operated to pump water 
out of the system. The result is that cavitating con- 
ditions can be maintained in the working section 
for any desired test velocity. There is an air bleed line 
at the top of the 5-ft diameter tank, as shown in 
Figure 12. This is opened, upon filling the system, 
when the air in the tank is being displaced by water. 
For low-pressure operation a Nash Hytor vacuum 
pump is used in the bleed line to remove any accumu- 
lations of air that may gather in the system. 

Cooling Circuit 

In the operation of the tunnel, up to 250 hp is 
continuously put into the system through the circu- 


lating pump. This energy is all dissipated into heat; 
thus, unless the system is cooled, the temperature will 
rise to undesirable values. To maintain a constant 
temperature and therefore constant viscosity at the 
Reynolds number for testing, this heat must be re- 
moved. The method for doing this is also shown in 
Figure 5. A part of the return flow from the by-pass 
valve of the pressure-regulating system goes to the 
cooling water pump, which circulates it through a 
forced-draft cooling tower on the roof and returns it 
to the storage tanks. Thus cooling is obtained by con- 
tinuously bleeding off heated water from the system 
and returning an equal amount of cooled water. 

Balance 

Principle and General Arrangement 

As previously outlined, the balance is designed to 
measure three components of the hydrodynamic 
forces operating on the model. These are the drag 
force parallel to the flow, the cross force normal to the 
flow, and the moment about the axis of support. Note 
that these components are with reference to flow 
direction and not to the model orientation. Figure 18 
is a diagram of the balance system. Basically, it con- 
sists of a vertical spindle supported near the center 
with a universal pivot that permits rotation through 
any axis about this point but allows no translation. 
The model is attached rigidly to the top of the spin- 
dle. This assembly is prevented from rotating under 
the action of the hydrodynamic forces by applying 
restraining moments about three mutually perpen- 
dicular axes intersecting at the pivot. These moments 
are applied by hydraulic pressure through the three 



Figure 17. Working section after assembly. Front view. High-speed water tunnel. 



HIGH-SPEED WATER TUNNEL 


17 


sets of pistons, cylinders, and yoke wires as shown in 
Figure 19. The three restraining moments correspond 
to the hydrodynamic forces acting on the model. In 
order to measure the forces acting on the model when 
it is inclined to the flow, the vertical spindle was made 
in two pieces. The model is attached to the upper 



Figure 18. Diagram of balance system, high-speed 
water tunnel. 

piece while the supporting pivot and pressure cylin- 
ders are attached to the lower piece. By rotating the 
upper spindle section with respect to the lower one 
and clamping it securely in place, the angle of yaw of 
the model is changed with respect to the flow but -the 
direction of the balance restraining forces remains 
unchanged. 

In order to keep the model position accurately 
fixed in the flow while the measurements are made, 
the limits of motion of the hydraulic pistons are 


restricted to ±0.003 in. This is equivalent to less 
than 2 minutes of angle. These small deflections re- 
quire great structural rigidity, both of the spindle 
and of the supporting frame. Figure 15 shows how 
this rigidity has been built into the structure. The 
whole assembly is mounted on a hydraulic lift for 
ease in handling and adjusting. It is completely sup- 
ported by this lift in the working section even when 
in position for measurements. 


Spindle 

The spindle which supports the model is seen pro- 
jecting vertically upward from the top of the balance 
in Figure 20. This spindle is removable so that dif- 
ferent types can be installed to meet the varying 



Figure 19. View of balance showing application of 
moments by hydraulic pressure to balance system. 
High-speed water tunnel. 

needs of the different tests. The spindle pivot point 
lies at the center of the bronze ring seen at the top of 
the structure. The pivot is made up of two sets of 
three pairs of piano wire. Each set forms three equally 
spaced elements on the surface of a cone. The two 
vertices meet in a point on the centerline of the spin- 
dle. This means that for small deflections this point is 
the center of rotation for all three moments that are 
measured, and the resistance offered by the deflection 
of the support wires for slight angular movements of 
the spindle is small. Two pairs of wires can be seen in 
Figure 20. 


Seal 

A watertight seal is provided between the balance 
spindle and the working section in the form of a soft 
rubber cylinder which is reinforced with concentric 


/UON a17J 


18 


LABORATORY FACILITIES 


steel rings vulcanized into it. This construction per- 
mits extreme flexibility and, at the same time, gives a 
structure which will resist both internal and external 
pressure. It operates satisfactorily from gauge pres- 
sures of 50 psi down to the vapor pressure of cold 
water. This seal is illustrated in Figure 21, which 
shows the deflection of the cylinder under the com- 
pression of a C clamp. 


Yaw Angle Ad.tustment 

The angle of yaw of the model is changed by the 
rotation of the upper spindle with respect to the 



Figure 20. Balance spindle. High-speed water tun- 
nel. 


lower spindle, over a range of about —20 degrees to 
-1-20 degrees. The two spindles are held together by 
aspring-loaded brake which has a resisting torque 
greater than any hydrodynamic moment within the 
design capacity of the balance. 

The process of angle changing then requires that a 
torque be applied between the upper and lower spin- 
dles which will slip the friction brake. This torque is 
supplied by an electric motor mounted on the lower 
spindle. The motor operates a worm which engages a 
sector integral with the upper spindle, thereby slip- 
ping the brake and turning the upper spindle with 
respect to the lower spindle. The control buttons for 
angle changing are clearly shown in Figure 22, as 
well as the angle-changing motor. 


The angular position of the model is indicated to 
the nearest 0.1 degree by a dial gauge attached to the 
lower spindle and having its deflection rod connected 
to the upper spindle by means of a flexible ribbon 
wound around the upper spindle. This dial gauge is 
the larger one shown in Figure 22. 

Force- and Moment-Transmitting System 

The hydrodynamic moments on the upper spindle 
are balanced by the restraining wires at the bottom of 
the lower spindle as shown in Figure 19. The wires 
and yokes shown here transmit the forces to the hy- 
draulic pistons. The length of the wires is great com- 
pared to the range of movement of the end of the 
spindle so that no error is introduced into the 
data. 

At the extreme right of Figure 19 is seen a pre- 
loader. This device applies a spring preload of 50 psi 



Figure 21. Watertight seal between balance spindle 
and working section. High-speed water tunnel. 


to the oil in the cylinder and, at the same time, com- 
pensates for the small but undesired elastic resisting 
moment exerted by the spindle pivot wires on the 
spindle during the small angular deflections incident 
to the balancing operation. The preload is needed so 
that positive and negative forces may be measured 
by one piston. The cross force preloader is partially 
seen in Figure 19. 

The pistons and cylinders are shown also in Figure 
19. The piston and cylinder are lapped to a clearance 
of about 0.00004 in. To eliminate static friction the 
cylinders are rotated at constant speed by individual 
motors. 



HIGH-SPEED WATER TUNNEL 


19 


Pressure Gauges 
Principle of Operation 

The pressure in the cylinders on the balance are 
measured by weighing-type pressure gauges. A close- 
up view of one of these gauges is shown in Figure 23. 
The gauge consists essentially of a beam supported 
on a Cardon hinge pivot. The pressure to be meas- 
ured is applied through a piston attached to this 
beam. This piston, like the balance pistons, is fitted 
in a cylinder which rotates to avoid static friction. 
The force exerted by the oil pressure on the piston is 



Figure 22. View of working section and balance 
mechanism. High-speed water tunnel. 

balanced by pan weights applied to the end of the 
beam and also by a rider weight running on the beam. 
Unbalance of this beam results in unbalance of the 
optical-electrical control system which, in turn, 
starts a small electric motor and moves the rider 
weight until equilibrium is obtained. 


pose of the photocell system is to obtain control of the 
beam by frictionless and nonfouling means and at the 
same time to obtain a response of the rider weight 
motor in proportion to the unbalance or deflection of 



Figure 23. Weighing-type pressure gauge. High- 
speed water tunnel. 

GAUGE BEAM 



Figure 24. Schematic diagram of photocell control, 
high-speed water tunnel. 


Photocell Control 

The optical-electrical control of the equilibrium of 
the beam is obtained through use of a photocell system 
which is shown schematically in Figure 24. The pur- 


the gauge to avoid hunting. As can be seen by the 
schematic diagram, unbalance of the gauge causes a 
beam of light to move either to right or left and thus 
to give unequal illumination on the symmetrical 
halves of the phototube. This results in a voltage 


20 


LABORATORY FACILITIES 


which actuates a motor which moves the rider toward 
a balanced condition. At the balanced position, the 
two halves of the phototube are illuminated equally 
by the beam of light and thus there is no voltage to 
cause a movement of the rider. The position of the 
rider is indicated by a Veeder counter, and a scale is 
chosen such that the counter indicates the applied 
pressure directly in pounds per square inch to the 
nearest 0.01 psi. 

Sensitivity and Range of System 

The length of the balance lever arms and the areas 
of the pistons in the system have been chosen so that 
the readings of the drag and cross force gauges in 
pounds per square inch are numerically equal to twice 
the hydrodynamic drag and cross force in pounds 



Figure 25. Control panel. High-speed water tun- 
nel. 

and the reading of the moment gauge in pounds per 
square inch is numerically equal to the hydrody- 
namic moment expressed in inch-pounds. Pan weights 
are available in 50 psi units to a maximum of 500 psi, 
and the range of travel of the rider weight corresponds 
to 50 psi. 

Control Panel 

Figure 25 shows the instrument panel with the 
cross force, drag, and moment gauges just described 
and the differential pressure gauge, to be described 
later. In the center of the instrument group is a panel 
with lights indicating the state of balance of the 
gauges and other essential operating data. When all 
panel lights are out, a condition of gauge balance and 
general instrument readiness is indicated. Thereupon 


a button is pushed which stops the gauge rider motors 
so that the pressure readings may be recorded. 


Hydraulic Transmission System 

This hydraulic system composed of the balance 
pistons and cylinders, gauge pistons and cylinders, 



Figure 26. Compensator. Assembled view. High- 
speed water tunnel. 

and the connecting oil line is subject to slight leakage 
of the working fluid (light turbine oil) past the 
pistons. The leakage of the system is made up by 
compensators shown in Figures 26 and 27, so that the 
system is essentially a constant-volume one. The 



Figure 27 Compensator. Disassembled view. High- 
speed water tunnel. 

compensator is a small screw-operated pistoq which 
supplies oil to the system in a definite minute amount 
upon receiving an electric signal from the balance 
indicating that the amount of oil in the system has 
reached the minimum permissible. The indication of 



HIGH-SPEED WATER TUNNEL 


21 


the state of the oil system is made also by lights on 
the instrument panel. 

* ^ ® Balance Sensitivities 

In discussing the sensitivity of the balance system, 
two characteristics must be noted. The first is sensi- 
tivity defined as a change in the reading on the 
pressure gauge per unit change in force on the model. 
On this basis for the cross force and drag measure- 
ments, one dial division corresponds to 0.005 lb force 
on the model. For the corresponding moment read- 
ings, one dial division corresponds to 0.01 in.-lb 
torque on the model. The second characteristic is 



Figure 28. Schematic diagram of the differential 
pressure gauge, high-speed water tunnel. 


responsiveness, which is defined as the magnitude of 
the minimum impressed force on the model necessary 
to cause a change in the gauge readings. This re- 
sponsiveness is approximately 0.01 lb for cross force 
and drag measurements on the model and 0.02 in.-lb 
for moment. 

2.2.7 Differential Pressure Gauge 

Principle of Operation 

A differential pressure gauge is employed which is 
very similar in appearance and design to the pres- 
sure gauges described above. The only difference 
is that the force applied to the beam is the result 
of the difference of two pressures applied to the 


opposite ends of a piston. Figure 28 is a schematic 
diagram of this differential pressure unit. The two 
pressures are applied, one at the top and one at the 
bottom of a piston and the resulting force on the 
piston depends on the difference between the two 
pressures. This resulting force is transmitted to the 
beam and is measured in the same way as in the 
pressure gauges described above. The cylinders, like 
those used in the force measuring system, are rotated 
to avoid static friction. The gauge is actuated by oil 
connections from two bodies of oil floating on water 
surfaces in cylindrical separating pots beneath the 
gauge itself. The pressure leads from the water tunnel 
are connected into these separating pots. The pots 
are horizontal to permit a large change in volume 
with a relatively small change in elevation of the oil- 
water interface. This is necessary since, due to the 
different densities of oil and water, the reaction of the 



Figure 29. Three-hole direction-finding pitot tube. 


gauge will be affected by changes in the height of the 
oil columns. A cross connection between the two 
reservoirs permits initial leveling of the system. 

Applications 

The principal application of this differential pres- 
sure gauge is in the measurement of velocity of flow 
in the working section by means of the pressure dif- 
ferences across the nozzle. Other applications are in 
the measurement of the pressure distribution on pro- 
jectile models and in the measurement of the pressure 
and velocity distribution across the working section, 
which is obtained with the three-hole direction-find- 
ing pitot tube shown in Figures 29 and 30. Since this 
is essentially a zero volume-change device, the re- 
sponse of the gauge to pressure changes is very rapid. 

^ ^ ® Pressure Distribution 

Measuring Equipment 

Since measurements are made on the model with a 
fluid flow having a pressure gradient along the work- 



22 


LABORATORY FACILITIES 


ing section and since the size and position of the 
model affects this pressure gradient, it is necessary to 
measure the pressure in the working section at closely 
spaced points along the wall. For this purpose the 
multiple differential manometer, seen in Figure 31, is 
employed. This is an air- water type with all columns 
having common air connections, and in general the 
pressure at the beginning of the working section is 



Figure 30. Three-hole pitot tube mounted for use 
with high-speed water tunnel. , 


used for the reference pressure. Figure 31 also 
shows that the multiple differential manometer is 
well suited for photographic recording. Since the 
total pressure drop in the working section is of the 
order of 0.1 or 0.2 of a velocity head, great care has 
to be exercised in the construction of the piezometer 
openings to insure that the static pressure alone is 
measured, without measuring any of the velocity 
pressure. 


Shields 


In order to avoid corrections for hydrodynamic 
forces on the exposed spindle within the working 
section it is necessary to install streamlined shields 



around the spindle, firmly attached to the working 
section. This shield must be as small as possible in 
order to minimize disturbances in the flow, yet there 
must be sufficient clearance between the spindle and 
the shield so that there is no chance of the shield 
touching the spindle and absorbing a portion of the 



HIGH-SPEED WATER TUNNEL 


23 


hydrodynamic forces applied on the model. The shield 
in present use for force tests is shown in Figure 32. 
This photograph shows the shield, spindle, and model 
installed, and Figure 33 shows a dummy shield, 



» ^ * » * • .-_J[ 


Figure 32. Shield, spindle, and model installed in 
water tunnel. 

termed an image shield, mounted above the model, 
and used in the tests to determine interference 
corrections. The shield is made in two sections, 
the section next to the model being much smaller 



Figure 34. Shield used in connection with visual 
observation of cavitation. 


than the section mounted on the tunnel wall. Both 
sections are Joukowski streamlined shapes. A splitter 
plate between the two sections acts to prevent cross 
flows. The purpose of the design, termed a duplex 
shield, is to secure a minimum flow disturbance 
near the model by use of the small upper shield, 
yet to allow use of a spindle size large enough to 
prevent undue deflection. The radial clearance be- 


tween the spindle and the inside bore of the shield is 
about 0.015 in. Figure 34 is a photograph of a shield 
used for visual observation of cavitation. Since no 
forces are measured during visual cavitation tests. 



^ ^ ^ ^ SI 

Figure 33. Shield, spindle, and model group with added 
image shield (above model) installed within the tunnel. 


the model is mounted rigidly to the shield and the 
large-diameter spindle is unnecessary. Therefore, this 
shield can be considerably more slender than the 
force shields. Note that the model is mounted di- 



Figure 35A, B. Typical two-dimensional models, dif- 
ferent lengths of an NACA 4412 airfoil. 

rectly on the top of the shield and thus in effect the 
model is fastened rigidly to the working section. This 
shield is a streamlined, cavitation-resistant shape de- 
veloped by the David Taylor Model Basin. In addi- 




24 


LABORATORY FACILITIES 


tion to the two types of shields described above, 
a shield has been developed for the simultaneous 
measurement of cavitation and force data. This 
shield also is a cavitation-resistant David Taylor 
Model Basin shape, and the spindle employed is 
elliptical in cross section so that for small angles of 
yaw the required rigidity is combined with the nec- 
essary slenderness. 

2.2.10 ^ater Tunnel Operating Techniques 
Models 

The models used are exact geometric replicas of the 
prototypes within the tolerances of the precision 
machine shops employed. Most of the models have 
been three-dimensional but some two-dimensional 
testing has been done. Figure 35 shows two typical 



Figure 36. Typical 2-in. diameter model assembled 
about support section. 

two-dimensional models, different lengths of a NACA 
4412 airfoil. In this application, flat plates were in- 
stalled in the bottom and top of the working section 
for the full length and the two-dimensional model 
spanned the distance between these two plates. This 
special setup was necessary in order to avoid end 
effects and thus secure pure sectional or two-dimen- 
sional data. The three-dimensional models are fas- 


tened securely to the spindle in the following manner: 
A 2-in. diameter model section is silver-soldered to 
the end of the spindle and the remaining parts of the 
model are fastened to this center section by means of 
a through bolt. 

Figure 36 shows a typical model and Figure 37 
shows the individual components including the spin- 
dle and integral center section. A complete set of 



Figure 37. Same as Figure 36 but with model parts 
separated. The central cylindrical section is fastened 
to the spindle. 


cylindrical body sections from 0.10 in. to 0.20 in. long- 
in 0.01-in. steps and from 0.20 in. to 4.00 in. in longer 
steps is available so that any cylindrical length may 
be readily made up. The necessary nose, afterbody, 
and tail members are fastened to the cylindrical part 
by means of a bolt through the whole assembly. The 
individual components have tongue and shoulder 
joints to secure precise alignment. A concentricity of 
about ±0.0002 in. has been secured. When a design 
of a new body is submitted for test, a quick survey of 
the model parts shows what elements are available 
and what new parts must be made. In general the 
model parts are made of stainless steel to eliminate 
corrosion and to secure a reasonable hardness to pre- 
vent damage from handling. Special sections may be 
made of brass. Figures 38 and 39 show a typical 
powered model with an exhaust stack in which a flow 
of compressed air simulates the turbine exhaust. The 
motors used for the powered models are of a high- 
cycle induction type. 






HIGH-SPEED WATER TUNNEL 


25 


Operating Variables 

The following quantities concerned with model 
performance may be varied conveniently with the 
existing equipment in the water tunnel: speed, pres- 
sure (submergence), pitch angle, yaw angle, rudder 
angle, and geometry of the model. Most of the tests 
conducted in the laboratory involve a systematic in- 
vestigation of the effect of one of these variables while 
all the others remain constant. 



Figure 38. Typical powered model with exhaust stack 
for compressed air simulating turbine exhaust. 



Figure 39. View of tail showing propeller and ex- 
haust pipe. 

Force Tests 

The fundamental test in the laboratory, termed a 
force test, involves a study of the hydrodynamic 
forces acting when speed, pressure, pitch angle, rud- 
der angle, and geometry are constant, and yaw angle 
is the variable. In this test the yaw angle of the 
model is varied from about —15 degrees to -f 15 de- 
grees in 2-degree increments and the forces (drag, 
cross force, and moment about the support point) 
are read simultaneously with the velocity on the pres- 


sure gauges at the instrument panel. Instead of the 
yaw angle being the variable, the pitch angle may be 
made the variable by simply rotating the model 
about its longitudinal axis until the pitching plane of 
the model is horizontal. This test is then conducted in 
the same way as the yawing test. In addition, the 



Figure 40. Typical plot of a force test. 


rudder angles may be successively varied from up to 
down or from port to starboard to obtain this effect 
superimposed upon the effect of yaw or pitch angle. 
Studies may be made of models with successive 
changes in components such as nose shape or fin size 
in order to obtain the effect of the model geometry. 
The results of the tests are plotted as they are ob- 
tained. Figure 40 is a typical plot of force test. 


G]fatNrii>i:vrmn 


26 


LABORATORY FACILITIES 


Speed Tests 

Tests are also made in which the principal variable 
is speed. In this case the hydrodynamic forces on the 
model are obtained for a speed range of from 10 to 70 
fps, usually in 5-fps increments. Here again different 
model components may be tested in order to obtain 



Figure 41, Typical plot from a speed run. 


the effect of the model geometry upon the speed per- 
formance. Figure 41 shows a typical result of one of 
these tests. 

Cavitation Tests 

The effect of pressure (prototype submergence) 
may also be determined in the laboratory by the 
cavitation test. Usually this test is made with the 
model securely fastened to the working section and 
no forces are measured. The speed is held constant 
and the pressure in the working section is varied by 
means of the motor-controlled by-pass valve as ex- 
plained in the description of the pressure-regulating 
circuit. The absolute pressure in the working section, 
at which various cavitation phenomena occur, is re- 
corded both photographically and visually. Figure 42 
illustrates typical photographs obtained in the cavi- 
tation tests. A series of such pictures clearly shows 
the nature of the cavitation on the projectile at the 
speed and depth indicated by the cavitation para- 
meter K. In this way the cavitation performance of 
various model components may be studied or the 
occurrence of cavitation may be determined for 
various model parts as a function of yaw or pitch 
angle. Figure 43 is a plot showing cavitation para- 
meter K at which cavitation occurs on the tail of a 
torpedo, as a function of the yaw angle of the pro- 
jectile. In recent months a shield and spindle has been 
designed which permits the measurement of the 
hydrodynamic forces under cavitation conditions. In 


such a test, in addition to the photographic records of 
cavitation obtained, the hydrodynamic forces are 
measured at the same time. Thus it is possible to test 
models where yaw or pitch angle and pressure are 
both variables. 



Figure 42A, B, C. Typical photographs obtained in 
cavitation tests. 



9 

< o 
z 
o 


UJ w 


Figure 43. Plot showing the cavitation parameter, K, 
at which cavitation occurs on the tail of a torpedo, as a 
function of yaw. 


Pressure Distribution Tests 

Tests are also made to determine the pressure dis- 
tribution about the surface of models. In this case 
the model is securely fastened to the working section 
through the shield as in the cavitation test. The sur- 




THE POLARIZED LIGHT FLUME 


27 


face of the model has numerous pressure taps drilled 
normal to it and the pressure is transmitted from the 
model by means of small-diameter copper and rubber 
tubing through the shield to a manifold. From the 
manifold, copper tubing leads to the differential pres- 
sure gauge and, by means of appropriate valving, the 
pressure difference between the surface at any point 
and the pressure in the undisturbed stream may be 
obtained. The complete pressure distribution about 
the model is determined this way. A complete pres- 
sure distribution is usually made for successive yaw 
or pitch angles. 

Powered Model and Exhaust Tests 

Powered tests and exhaust tests have been con- 
ducted in the water tunnel in an effort to determine 
the interaction between exhaust jets and propellers. 
In this test the speed, pressure, yaw angle, and pro- 
peller revolutions per minute are held constant and 
photographic evidence of the interaction of jet and 
propeller is obtained for various air flows through the 
jet and various arrangements and dimensions of 
exhaust stack. 


2-^ THE POLARIZED LIGHT FLUME 

^ ^ ^ Comparison of the Polarized 

Light Flume with the High-Speed Water 
Tunnel and the Free-Surface Water Tunnel 

The polarized light flume is essentially similar to 
the two large tunnels in that it furnishes a working 
section in which observations can be made on bodies 
immersed in a flowing liquid. It is so arranged that 
the upper surface of the working section can either be 
closed with a solid boundary like the high-speed 
water tunnel, or left free to the atmosphere as in the 
free-surface water tunnel. It is, however, a very much 
smaller piece of equipment as can be seen by the 
comparisons shown in Table 1. 


Table 1. Comparison of flume and tunnel characteristics. 



Working section 


Max 



Cross 

Max 

rate of 

Max- 


section Length velocity 

flow 

imum 


in sq ft in ft 

in fps 

in cfs 

hp 

High-speed water 

1 6 

75 

75 

250 

tunnel 

Free-surface 

3 8 

25 

75 

75 


water tunnel 

Polarized light flume 4 6 3 2 


^ ^ Principle of Operation 

The distinctive feature of this flume is that instead 
of pure water, the circulating fluid is a dilute sus- 
pension of bentonite. This is for the purpose of mak- 
ing the flow visible. Certain grades of bentonite have 
correlated physical and optical asymmetries. The 
physical asymmetries are such that if the particles 
are suspended in a stream of water, any relative shear 
between two adjacent filaments of water will tend to 
align the particles in a given orientation. The optical 
properties of the particles are such that if light is 
passed through the stream, the light waves will be 
rotated an amount proportional to the thickness of 
the fluid layer and to the degree of uniformity of the 
orientation of the particles. If the light used is 
polarized, the results will be a pattern of bands which 
is characteristic of the shear pattern existing in the 
fluid, and since this shear pattern is directly associ- 
ated with the velocity distribution, the optical pat- 
tern gives a good approximation of the velocity field. 
Figure 44 is a diagrammatic sketch of the scheme of 
observation. It will be noted that Polaroid screens 
are placed on either side of the working section. 
These may be used either with or without one- 
quarter wave plates since very similar results can be 
obtained with either plane or circularly polarized 
light. The polaroid screens can be so oriented with 
respect to each other that the pattern will be shown 
either in black and white or in color. 

^ ^ Construction of the Flume 

Although only a very small amount of bentonite is 
required to produce a suspension having the desired 
characteristics, it introduces some very undesirable 
complications. The suspension reacts with a large 
number of metals. This results in corrosion, but an 
even more serious effect is that it causes the bentonite 
suspension to thicken and coagulate and thus de- 
stroys its use for the study. Unfortunately iron and 
nearly all its alloys, including stainless steel, react 
with the bentonite. Lead and tin mixtures also react, 
which eliminates the use of soldered joints. The polar- 
ized light flume, therefore, was constructed entirely 
of brass with silver-soldered joints, with glass walls in 
the working section. Figure 45 shows a photograph of 
the flume and Figure 46 is a line drawing of it. The 
suspension is circulated by a small propeller pump. 
This pump is a standard commercial design but made 
of brass instead of the cast iron usually employed. It 


28 


LABORATORY FACILITIES 



Figure 44. Cross section of polarized light flume. 


DIFFUSING 

SCREEN 



is driven by a standard induction motor with an 
integral variable-speed V-belt drive which gives a 
speed range of 172 to 1,200 rpm. The velocity, of 
course, varies in the same ratio. Lower velocities are 


obtained by adjusting a four-leaf pyramid type of 
valve which is installed on the inlet side of the 
propeller. Two views of this valve are shown in Fig- 
ure 47. The pump discharges into a diffuser section 



Figure 45. The polarized light flume. 


THE POLARIZED LIGHT FLUME 


29 



I 2 S 4 

Figure 46. Elevation of polarized light flume. 


which reduces the velocity to a very low value with a 
corresponding increase in cross section. The flow is 
brought to the working section at this low velocity by 
means of two vane elbows. The flow is accelerated to 
the velocity of the working section by a nozzle having 
a rectangular cross section. The contraction ratio of 
this nozzle is 43^ to 1. 

The working section is followed by a diffuser sec- 
tion which is operated with a free surface. An at- 
tempt is made to regain as much energy as possible in 
this section. This is done not so much to save the 
small amount of energy involved, but rather to elimi- 
nate all possible sources of disturbance which may 
carry around through the pump and passages to the 
working section. From the diffuser section the flow 
goes through the valve to the inlet to the propeller 
pump which has already been described. 

^ Working Section 

The working section employs glass plates for the 
two sides and the bottom. A Lucite cover has been 
constructed which can be installed as a prolongation 
of the upper surface of the nozzle when it is desired to 
operate the flume as a closed channel. It has been 
found more convenient for most studies to operate 
with the free surface to permit the easy insertion of 
auxiliary equipment for studying the details of the 
velocity distribution. A horizontal spindle has been 
mounted on the rear side wall to support the models. 
This is equipped with a streamlined shield of the 
same cross section as the one used in the high-speed 
water tunnel. The spindle can be rotated by a worm 


and wheel on the front of the working section, thus 
permitting the observation of the flow pattern as it is 
affected by pitch or yaw. The degree of rotation is 
measured on a protractor which is an integral part of 
the rotating mechanism. This equipment can be seen 
in Figure 48, and also in Figure 49 which shows a 
close-up of the working section. The spindle is con- 
structed so that the models used in the high-speed 
water tunnel may be installed in the polarized light 
flume without alteration. Although these models are 
made of stainless steel, it has been found that they 
can be used in the bentonite suspension without 
harm, either to themselves or to the suspension, if 
care is taken to leave them in for short periods only 
and if they are washed and dried thoroughly after 
each use. The two polaroid screens are supported, one 
on each side of the working section, by a carriage 
which rolls along guide rails mounted on the top of 
the flume. These screens are 12 in. high and 30 in. 
long, and thus provide a working area that is suffi- 
ciently large for most observations without the need 
of readjusting their position. Provision is also made 
for carrying the light source on the same carriage. A 
rear view of this light source is seen in Figure 50. 
For normal observations a battery of incandescent 
lights is used, but for special purposes high-intensity 
lights or high-voltage flash lamps may be employed. 

Applications 

of the Polarized Light Flume 

The majority of results of the studies made in this 
flume are reported in the form of sketches of the flow. 


30 


LABORATORY FACILITIES 



In order to assist in the preparation of these sketches, 
the guide rulings of Figure 51 are mounted on the 
side windows of the working section. A miniature 
drafting machine of the steel-tape type is attached to 
the carriage as shown in Figure 52. It is used largely 


clear indication of the local flow angle. The mecha- 
nism, removed from the flume, is seen in Figure 53. 
Another technique that has been found useful is the 
introduction of minute air bubbles into the flow by 
the use of a very fine tube. At the velocities used for 
the studies the path of these air bubbles is very easily 
followed. Great care must be exerted to keep these 
bubbles small, however, since if their size becomes 
appreciable, their velocity of rise will become signifi- 
cant in comparison with the velocity of flow and thus 
distort their indications. Figure 54 shows the same 
typical bubble paths. 


Figure 48. Pitch angle control and protractor for 
polarized light flume. 


Principles of Operation 


Streaming Double Refraction 


Figure 47.A, B. Four-leaf pyramid-type valve used 
with polarized light flume. (A) Closed. (B.) Open. 

for determining the angles of flow in the various parts 
of the field. For detailed studies of the flow the indi- 
cations of the polarized light patterns have been 
supplemented by other methods of delineating the 
flow. One of these is a mechanism for moving a small 
probe to any desired point in the working section. 
This probe carries a short section of light thread 
which streams out parallel with the flow and gives a 


It is a well known fact that certain crystals possess 
the optical property of producing double refraction 
when a light beam is passed through them. The 
magnitude of the effect depends upon the length of 
the light path. A given length of light path could be 
obtained by the use of a single crystal of the proper 
dimensions or a series of crystals which, when added 
together, made up the required length. The total 
effect would be the same provided that in the case of 
the multiple crystals their optical axes were oriented 
in the same direction. If, however, their axes were 
oriented at random, no double refraction would be 
observed because the effects of the different crystals 
would cancel each other. If such a system of crystals 
were suspended in the fluid, double refraction would 
still take place. The magnitude of the effect observed 


CONFIDENTIAL 




THE POLARIZED LIGHT FLUME 


31 


would depend upon the uniformity of the alignment 
of the axes of the crystals along the given optical 
path. It is apparent that if the optical alignment of 
the crystals were dependent upon some property of 
the flow of the fluid, a valuable tool would become 
available for the study of fluid flow. A brief considera- 
tion will show, however, that if a crystalline material 
is to fulfill the requirements, it must possess some 
unique characteristics. In the first place, the crystals 
must possess the property of double refraction. 
Second, the individual particles must be single crys- 
tals or masses of crystals so oriented that the}^ be- 
have optically as a single crystal, i.e., their optical 
axes must be parallel. Next, they must be insoluble in 
the fluid in which they are to be used. If the flow of 
the fluid is to have any effect on their alignment, they 
obviously must be physically asymmetrical. Further- 
more, if this physical asymmetry is to be effective, it 
must have a uniform correlation with the optical 
asymmetry. If this phenomenon is to be used as a 
tool for the study of flow, it is necessary that the 
presence of the crystals should have little or no effect 
upon the flow. This means that the individual parti- 
cles must be small, i.e., their dimensions should be of 
the same order or smaller than the least dimension 
required to measure the characteristics of the flow. 


and their path must conform to that of the flow. This 
means either that the density of the crystalline ma- 
terial must be the same as that of the fluid or else that 
the individual particles must be so small that their 
fall velocity will be negligible as compared to the 
velocity of the fluid. The ideal case would be to have 
the particles so small that they would fall in the range 
of the Brownian movements and thus form a perma- 
nent suspension. 

Assuming that such material were available, how 
could it be used? It would be very desirable if it could 
be made to indicate the velocity of flow. However, a 
brief consideration of the flowing suspension indicates 
that this is not possible. Consider a stream of this 
suspension flowing at a uniform velocity without 
turbulence. In this case all of the elements will be 
flowing at exactly the same velocity in parallel 
paths, and therefore will have no tendency to alter 
the orientation of the individual particles suspended 
in the fluid. This still holds true if the velocity of the 
entire flow is raised or lowered to any desired value. 
It is only when two adjacent layers of the fluid are 
considered to flow at different velocities that any 
force rises which can alter the orientation of the sus- 
pended particles. If the suspended particles are asym- 
metrical, say needle-like or plate-like in form, it is 



Figure 49. Close-up of working section of polarized light flume. 


32 


LABORATORY FACILITIES 



obvious that the difference in velocity between the 
two fluid layers will tend to produce uniform align- 
ment of the particles lying in this boundary. It is 
reasonable to suppose that the number affected and 
degree of uniformity of alignment will be related to 
the magnitude of the difference in velocity of the two 


Figure 50. Rear view of light source for polarized 
light flume. 

layers. It will be seen from these considerations that 
the information which can be obtained by the use of 
this tool will concern the velocity differences or shear 
in the flow rather than the velocity itself. In general, 
the average velocity of the flow will be known or, at 
least, the velocity in some given location. If this is the 
case, then the knowledge of the velocity differences 
can be used to determine the velocity field over the 
entire flow. There are many limitations to the use of 
this method of flow study. The instrument used to 
obtain information from the flowing suspension is a 
beam of light which traverses the flow from one 
boundary of the channel to the other. The optical 
effect on the beam must be the summation of all the 
effects along the entire path. If these effects are uni- 
form, the overall results will be measurable. If they 
are completely at random, the overall results will be 
nil. This indicates that the simplest use of streaming- 
double refraction is for the study of two-dimensional 
flow. Furthermore, if the flow is turbulent, the turbu- 
lent components will introduce a random disturbance 
which will affect the observation. Experiment has 
shown that it is possible to use this method for 
quantitative measurements in two-dimensional lami- 
nar flow. To do this it is necessary to measure the 
relationship between the rate of shear and the double 
refraction obtained along a given length of path. 


Qualitative measurements are possible in two-dimen- 
sional turbulent flow, although quantitative meas- 
urements are not yet feasible. At first glance it would 
appear that measurements of any kind would not be 
possible in three-dimensional flow, although experi- 
ence has shown that good qualitative measurements 
can be made. In this connection it is interesting to 
observe that single photographs of three-dimensional 
flow are usually quite disappointing as compared 
with the results obtained from direct visual observa- 
tion. There are apparently two reasons for this. One 
is that binocular vision makes it possible to differenti- 
ate between the flow characteristics at different 
distances in spite of the fact that each individual light 
ray gives only the integrated effect. The other is that 
persistence of vision gives quite a strong differentia- 


Figure 51. Guide rulings for polarized light flume. 

tion between the steady flow pattern around the 
body and the random-motion characteristic of a 
turbulent motion which overlays the picture. Of 
course, the presence of turbulence is not a necessary 
accompaniment of three-dimensional flow. However, 
in all of the uses made of this method of study by the 



THE POLARIZED LIGHT FLUME 


33 


laboratory, it has been felt desirable to use turbulent 
flow since the indications obtained from purely 
laminar flow would have been of little practical value. 
As stated in the introduction to this section, the flow 
is actually observed through the use of circularly 
polarized light. The reason for this is that the phenom- 
enon of streaming double refraction is essentially one 
of polarization. Therefore, if the flow is observed 
through a beam of light having a fixed image by 
polarization which can be produced by placing polar- 
izing plates on each side of the flume, then any 
change in the degree of polarization produced by the 
suspension in the flume will be readily visible. Figure 
55 shows the general appearance of the working sec- 
tion as observed by polarized light. Figure 56 shows 
the same model the instant after the motor was 



Figure 52. Miniature drafting machine attached to 
carriage of polarized light flume. 


started, but before the general turbulence level had 
had time to form. 

2.3.7 Development of the Use of Bentonite 

Development of the Use of Bentonite for 
Streaming Double Refraction 

There are undoubtedly many materials which 
possess the property of double refraction and which 
can be found or produced in suitable states to permit 
the necessary correlation between the physical and 
optical properties so that they can be used for 
streaming double refraction studies. Thus, for ex- 
ample, sesame-seed oil has this property to a limited 
extent. However, very few materials have as yet 


been developed which possess the required properties 
to such a degree that they become convenient for use 
in flow studies. One of these materials is bentonite. 
This is a clay-like mineral which has several in- 
dustrial uses. Its properties were studied rather in- 
tensively in the Chemical Engineering Laboratory of 



Figure 53. Probe mechanism, removed from polarized 
light flume. 

the Massachusetts Institute of Technology [MIT]. 
One of the results of these studies was that certain 
samples of the mineral showed strong properties of 
streaming double refraction. 

The MIT studies had indicated that different 
samples of bentonite showed widely varying amounts 
of streaming double refraction. At the beginning of 
the laboratory’s use of the material it was believed 
that all bentonite found in the California mines pos- 
sessed the property to a usable degree. This was soon 
found to be false. In fact, most of the samples tested 
from all sources showed too small an effect to be 
satisfactory. Because of a series of changes of distribu- 
tors, the source of the material which had given such 
successful results was lost. However, it was finally 
traced and proved to be material marketed under the 
trade name of M. S. Eyrite. The reason for the wide 
variation of the properties of materials from different 



Figure 54. Typical bubble paths observed in polar- 
ized light flume. 


sources is not known. It is suspected, however, that it 
is connected with its method of formation or with its 
subsequent history as it has affected the correlation 
between the physical and optical asymmetries. Thus, 
for example, if the very fine individual particles have 
been formed by some grinding or disintegrating pro- 



34 


LABORATORY FACILITIES 


cess that largely destroyed the correlation between the 
physical and optical asymmetry, the material would 
show little streaming double refraction. The concen- 
trations of the M. S. Eyrite required for use in the 
6-in. wide laboratory flume have been quite low. The 
suspensions used for most of the work have contained 
approximately 0.1 to 0.2 per cent of the bentonite. In 
all cases the liquid used has been pure water. This 
amount of bentonite has the effect of increasing the 
viscosity slightly. During the useful life of the sus- 
pension it appears that the viscosity is about doubled. 
This increase, of course, is not enough to be detected 
by qualitative means. Experiments showed that the 
suspension was somewhat sensitive to the mineral 
content of the water used. Suspensions made with tap 
water in the laboratory had a very short life, since 
after a few days’ use in the flume, when exposed to 


in suspension. After purification the material is di- 
luted to the proper concentration and is then ready 
for use. 

^ ^ * Tobacco Mosaic Virus 

The laboratory has been enabled to compare the 
properties of this bentonite with those of another 
material suitable for this use.^ The second material is 
tobacco mosaic virus. Semiquantitative tests showed 
that the virus has much greater properties of stream- 
ing double refraction than does the best of the ben- 
tonites. For example, 0.3 mg per cc of the virus gives 
approximately the same results as 3 mg per cc of the 
M. S. Eyrite. No quantitative measure of the increase 
in viscosity was obtained but the indications were that 
the virus produced little, if any, increase. One in- 



Figure 55. General appearance of working section 
of polarized light flume as observed by polarized 
light. 



Figure 56. Same model as in Figure 55 but at instant 
after motor started and before formation of general 
turbulence. 


the air, they commenced to flocculate. This was ac- 
companied by a rapid increase in the viscosity and 
decrease in the streaming double refraction. The use 
of distilled water eliminated this difficulty and ex- 
tended the life of the suspension to a couple of 
months. The deterioration of the suspension seems to 
be considerably accelerated by contact with air, since 
samples have been kept for long periods in closed 
glass bottles with no sign of deterioration. 

The bentonite is obtained either in the form of a 
coarse powder or in lumps. However, it is readily dis- 
persed in water by the use of a mixer of the Waring 
type. The individual particles of the bentonite are 
very fine, remaining in suspension indefinitely. How- 
ever, the material contains a considerable percentage 
of impurities. These are removed by passing the 
concentrated suspension through a continuous su- 
per-centrifuge at a moderate rate of flow. The im- 
purities separate out while the bentonite remains 


teresting observation was that an increase in the 
concentration above 0.3 mg per cc produced no ob- 
servable increase in the effect. This limited series of 
tests indicates that the virus is superior in several 
other characteristics to the bentonite. For equivalent 
suspensions the virus seems to be less cloudy and 
therefore transmits the light more effectively. Fur- 
thermore, the virus appears to be more stable, in that 
it did not show any signs of flocculation or change in 
properties with age, and its reaction to metals ap- 
peared quite neutral. On the whole, it was felt that 
the tobacco mosaic virus would be considerably su- 
perior to the bentonite for use on flow studies. Un- 
fortunately there is no commercial source of the 
material and it has not been possible to obtain a 
sufficient amount of it for a filling of the polarized 
light flume. 

Through the courtesy of W. M. Stanley of the Rockefeller 
Institute for Medical Research. 


CONFIDENTIAL 



THE POLARIZED LIGHT FLUME 


35 


^ ^ * Technique of Operation 

Standard Studies 

Most of the bodies studied in the polarized light 
flume were projectiles or projectile components. 
Standard studies consisted in delineating flow patterns 
for the projectile in two positions, i.e., with the axis 
parallel to and at an angle of 10 degrees with the flow. 
For determining the flow characteristics experience 
showed that the best visible indications were ob- 
tained when the velocity was about 1 fps. This low 
velocity, therefore, was used in the initial observa- 
tions to establish the general flow pattern. After 
this had been established by the operator, the ve- 
locities were increased to 4 or 5 fps to observe the 
effect of the change in velocity on the flow pattern, 
and especially on wake angles and similar details. 
During the delineation of these flow patterns auxili- 
ary methods of study were employed whenever 
necessary to clarify any details of the flow. 

Trouble-Shooting Studies 

In several cases the polarized light flume proved of 
value in locating the origin of disturbances, points of 
instability, etc., on projectiles which were giving un- 
satisfactory performance in the field. These studies 
followed the general pattern of the standard studies 
outlined, but detailed investigations were made on all 
points of possible trouble. Instead of making meas- 
urements for the two set angles only, it was often 
valuable to watch the flow as the angle of the axis 
with the stream was varied very slowly. 

Design of Stabilizing Surfaces 

The polarized light flume proved to be of assistance 
in aiding the designer to determine the optimum 
arrangement of certain types of stabilizing surfaces 
such as ring tails. In order to get the required stabili- 
zation with the permissible amount of drag, it is 
necessary to align the surfaces with the direction of 
flow at the place where it is desired to install them. 
Information was obtained in different regions by use 
of bubble streaks and thread probes. The angle of 
flow was measured by means of the small parallel- 
motion protractor installed on the permanent screen. 
Subsequent checks on models in the water tunnel 
showed that the angles determined in this manner 
were very reliable and that stabilizing surfaces in- 
stalled to conform with the flow as measured in the 


polarized light flume offered the minimum amount of 
drag, even when tested at velocities ten or more 
times higher than those at which the angles were 
determined. 

Flow Diagrams 

Owing to the difficulties outlined previously in ob- 
taining good photographs of the flow pattern, the 
results of the studies have been presented in the form 
of line diagrams of the flow. These diagrams are al- 
ways based on the actual observations and an effort 
was made to keep the flow directions correct. Figure 
57 shows a typical flow diagram. 

2 4 CONTROLLED-ATMOSPHERE 
LAUNCHING TANK 

Purpose 

The primary purpose behind the design and con- 
struction of the controlled-atmosphere launching 
tank is the securing of equipment that will permit the 
study of the hydrodynamic problems involved as a 
projectile enters the water from the air. All the speci- 
fications established at the beginning of the design 
were based on this objective. However, the equip- 
ment as it was finally constructed is useful for the 
investigation of other types of phenomena as well, in 
so far as they require the same facilities. The princi- 
pal auxiliary use that is evident is the investigation of 
underwater explosions. Such a study is obviously 
limited to the use of small-scale explosions to insure 
that the equipment will not be damaged. 

^ Analysis of Experimental 

Requirements 

Before the design of the equipment was initiated, 
careful study was given to the type of measurements 
that would have to be made in order to carry out such 
a series of investigations in the laboratory. Because of 
obvious limitations of space, it is necessary to use 
only projectiles of small dimensions for the study. 
However, if the results are to be useful, they must be 
applicable to projectiles of any desired size. It is a 
well-known fact that the various factors affecting the 
forces and motion of a free body do not all necessarily 
vary at the same rate as the size of the body is 
changed. However, it is often possible, if care is taken 
in establishing the conditions of the experiment, to 


36 


LABORATORY FACILITIES 


obtain similar conditions for all the significant forces 
for two systems that differ widely in their geometrical 
size. Previous to the construction of the controlled- 
atmosphere launching tank most of the laboratory 
studies of water entry of an air-flight projectile had 
been made with small-scale projectiles launched into 
an open tank at atmospheric pressure. A considera- 
tion of the force systems shows that this does not 
produce conditions similar to those acting on larger 
projectiles when similarly launched. The primary 
reason for this is that in the period immediately after 
the projectile enters the water it is not operating in a 



homogeneous fluid, but is acted upon by two fluids, 
that is, the water which touches it at the nose and 
possibly again at the tail, and the air bubble which 
surrounds the major part of the projectile surface. 
Now the shape and size of this air bubble is a function 
of the speed of the projectile which tends to keep the 
bubble open, and of the pressure in the surrounding 
water which tends to collapse it. This collapsing pres- 
sure is made up, not only of the hydrostatic pressure 
of the water at that point, but also of the superim- 
posed pressure of the atmosphere acting on the in- 
terface. In the case of a small-scale projectile 
launched into a tank at atmospheric pressure, the 
effect of this atmospheric pressure will be relatively 
greater than it will be for a larger projectile. This 
can be seen readily from a consideration of a simple 
numerical case. Assuming that the atmospheric pres- 
sure is equivalent to a column of sea water 33 ft high, 
consider a projectile that is one-half this length, i.e., 
163^ ft, and imagine that this projectile enters the 
water from the air and dives to a depth of 33 ft. It is 
now 2 projectile lengths beneath the surface. The 
absolute pressure in the surrounding water will be 2 
atmospheres, one due to its submergence and one due 
to the atmospheric pressure on top of the interface. 


Next consider a projectile similar in every respect to 
the first one except that it is 163^ in. in length instead 
of 163^ ft, i.e., every dimension has been reduced to 
one-twelfth of the original. Assume that it is launched 
into a water tank at atmospheric pressure and dives 
to a similar depth. If the depth is similar, the geo- 
metric relation must appear the same. This means 
that the small projectile should be two projectile 
lengths under the surface, i.e., 33 in. However, the 
pressure in the surrounding water will no longer be 
equal to that of a column of water twice as high as the 
submergence, but to a pressure equal to the sub- 
mergence plus 33 ft, i.e., to a column of water 13 
times as high as the submergence. Thus it is obvious 
that if the pressures are to be similar, the atmospheric 
pressure must be scaled down in the same ratio as the 
geometric dimensions were reduced. If this is not 
done, then there is no reason to suppose that the 
bubble which forms at the surface and surrounds this 
small projectile will be similar in size and in its effect 
on the forces acting on the projectile as the one sur- 
rounding the large-scale projectile. This is the funda- 
mental reasoning at the bottom of the decision to 
construct a launching tank in which the atmospheric 
pressure can be controlled to conform to the geo- 
metric scale of the projectiles being studied. Unfortu- 
nately the atmospheric pressure is not the only 
variable that may affect the behavior of a projectile 
at water entry. The density of the air is also a factor. 
Since the density of the water is constant, the density 
of the small projectile must be the same as that for 
the large one. This would indicate that the density of 
the gas forming the atmosphere should likewise re- 
main constant. This requirement is in direct contra- 
diction to that governing the change in pressure. The 
two can only be met by using a gas of great enough 
density so that when the pressure is reduced to cor- 
respond to the geometric scale, the density of the gas 
will be the same as that of air at atmospheric pres- 
sure. The conditions which make it possible to control 
the atmospheric pressure in the launching tank also 
make it possible to utilize gases other than air for the 
atmosphere over the interface. Another variable that 
may affect the characteristics at launching is the sur- 
face tension. Other factors may become evident upon 
further study of the problem. However, the initial 
considerations seem to indicate that of the various 
factors involved, the pressure is the one that is the 
most important and the density is next. It is antici- 
pated that the other factors will be of relatively little 
importance. 



CONTROLLED-ATMOSPHERE LAUNCHING TANK 


37 


^ ^ ^ Summary of Design Specifications 

In setting up specifications for this major piece of 
equipment it is convenient to subdivide it into four 
main components as follows: 

1. The tank. 

2. The launcher. 

3. The trajectory recording system. 

4. The data analyzing system. 

These components of course, are related ; for example 
some of the principal dimensions of the tank were 
determined by the decision to use photographic 
means for recording the trajectory. Again several 
types of launchers were eliminated because they were 
inherently too large and required too much space and 
adjustment to build them inside of a pressure vessel. 

Tank 

The basic specifications for the main tank were 
that it should permit a trajectory of approxi- 
mately 25 ft with a water depth of approximately 10 
ft. A distance of 12 ft was required from the launch- 
ing plane to the camera windows, with this distance 
kept as clear as possible of all obstructions that would 
interfere with the clear view of the cameras. As indi- 
cated in the previous section, the physical require- 
ments of the study called for scaling the atmospheric 
pressure down with the same ratio as the linear di- 
mensions of the projectile study. Since projectile 
scales of 12 or 15 to 1 were contemplated, this estab- 
lished the requirement that the tank should stand an 
external pressure of a full atmosphere. The installa- 
tion and operation of the launcher required that a 
large opening, which could be opened and closed 
rapidly, be provided in the top of the tank above the 
water line. 

Launcher 

The requirements for the launcher were largely 
dictated by the specific needs of the study. It was 
decided to adopt for the launching tank the standard 
2-in. model size used in the water tunnels. The maxi- 
mum velocity of entry was set at 250 fps. It was con- 
sidered desirable to make provisions for any tra- 
jectory angle from vertically downward to horizontal. 
Provisions were also required for launching the pro- 
jectile at any desired angle of pitch between 10 de- 
grees up and 10 degrees down from the trajectory 
angle. The desired accuracy of both the pitch and 


trajectory angles was established as one-fourth of a 
degree or less. It was decided that no adjustment for 
yaw and no provision for the introduction of angular 
velocity and pitch should be incorporated in the 
original launcher design, but that if possible, the de- 
sign should be laid out so that these adjustments 
could be incorporated later as they proved to be 
necessary. 

Trajectory Recording System 

It was realized that the models required for these 
launching studies would be more difficult and ex- 
pensive to construct than the projectiles for the water 
tunnel because they would demand not only all the 
high accuracy required for the water tunnel studies, 
but also high dynamic accuracy, i.e., they would also 
have to have the correct weight, specific gravity, and 
moments of inertia. Furthermore, each launching 
would carry considerable danger of damage to the 
projectile as a result of striking the tank at the end of 
the trajectory. All these factors pointed to the neces- 
sity of developing a trajectory recording system that 
would secure all the data possible with each launch- 
ing, even in the case of erratic trajectories. Therefore, 
the specification was established that the recording 
system should cover the entire underwater volume of 
the tank, as well as the above-water portion contain- 
ing the trajectory from the launcher to the water 
surface. It was decided to make an attempt to de- 
termine five components of motion, i.e., horizontal, 
vertical, and lateral movement, and rotation in the 
pitch and yaw planes. Since high angular and linear 
accelerations are to be expected during parts of the 
trajectory, it was established that recorder readings 
should be taken at the rate of about 3,000 per second. 

Data Analyzing System 

If detailed information is to be obtained from 
launching studies, it is unavoidable that each run 
will yield a large mass of data which must be ana- 
lyzed. It was apparent that the analysis of the data 
would require either a large staff of computers or 
special mechanical devices. The decision was made to 
follow the latter course. The requirements for the 
mechanical analyzer were that it should transform 
the readings of the raw data into increments of mo- 
tion along the path, analyzed into the five components 
outlined in the preceding paragraph, and, if possible, 
that this data should be plotted in the form of curves. 


38 


LABORATORY FACILITIES 


^ ^ Details of Construction 

A general view of the equipment designed to meet 
the specifications for the first three components is 
seen in Figure 58. This is a rendition of the tank with 
the launcher and recording system in place. 

Main Tank 

As will be seen from Figure 58, the main tank con- 
sists of a large horizontal cylinder along one side of 
which is fastened a section of a small cylinder. The 
purpose of the smaller cylinder is to provide the nec- 
essary distance from the cameras to the launching 
plane to permit the photographic recording of the 
trajectory. The larger cylinder is 13 ft in diameter and 
29 ft in length. It is made of Vie-in. steel plate with 
%-in. dished and flanged heads on each end. It has a 
6-ft by 20-ft opening along one side over which is 
welded the section of the 6-ft diameter cylinder. 
Special provisions are required to carry the hoop 
stress across the opening formed by the intersection 
of the two cylinders. This is done through the use of 
longitudinal T beams 20 in. high and running the 


entire 25 ft of the intersection. These beams transfer 
the loading into 2- by 12-in. vertical columns spaced 
at 54-in. intervals along the tank. The exact position 
of these columns was determined by careful study so 
as to place them to carry the load without eccentricity, 
but to keep them out of the field of view of the re- 
cording cameras. Four-inch H-beam ring stiffeners 
were welded around the circumference of the two 
cylinders in the plane of each column. To distribute 
the loading evenly over the floor of the laboratory, 
saddle feet were provided at each ring stiffener. 
Computation showed that with this method of 
support, no additional foundation would be required 
under the 6-in. reinforced concrete slab. The weight 
of the tank empty is approximately 40 tons, and when 
filled with water to the working depth of 10 ft, the 
weight is approximately 140 tons. Figure 59 is a 
sectional drawing of the tank. 

It will be seen in Figure 58 that there is a large 
rectangular hatch opening on top of the tank near the 
left end. This opening is 48 by 55 in. and is designed 
to permit mounting the entire launcher mechanism 
on the hatch cover. This opening is off center to in- 
crease the distance from the launching plane to the 



Figure 58. Controlled-atmosphere launching tank, Hydrodynamics Laboratory, California Institute of Technology. 



CONTROLLED-ATMOSPHERE LAUNCHING TANK 


39 


AIR TRAJECTORY CAMERA 



VEW UDOKING WEST 

Figure 59. Sectional view of controlled-atmosphere launching tank. 


camera. Very heavy reinforcing was required to carry 
the stress around this opening so as to prevent dis- 
tortion when the tank is used with pressure or 
vacuum. The hatch cover is hinged to the left-hand 
edge of this opening. Provision for opening and clos- 
ing it through a 90-degree arc is provided by a 12-in. 
hydraulic cylinder. When this cover is closed, a round 
rubber sealing ring recessed in the face of the cover 
prevents air leakage. This ring operates on the un- 
supported area principle. Heavy hydraulically oper- 
ated C-clamp frames are provided on the two longi- 
tudinal edges of the opening. They serve to hold the 
cover rigidly in place under either pressure or vacuum 
conditions during testing. Figure 60 shows the cover 
and clamps. Six 8-in. nozzles are welded to each edge 
of the 6-ft cylinder to permit the installation of Lu- 
cite tubes running from end to end of the tank. 
These are required to house the underwater lighting 
system. The tank is fitted with ten 12-in. openings for 
the addition of the recorder cameras. Five of these 
are located on a horizontal line on the side of the 6-ft 
cylinder midway between the stiffening rings. Three 
of the openings are placed above the water line near 
the hatch opening to cover the air flight, and one is 
placed at the centerline of each of the main cylinders. 
Four 16-in. access openings are provided along the 


upper portion of the main tank. Since the design of 
this tank was so unconventional, it was subjected 
after completion to a hydrostatic test of 60 psi. No 
signs of yielding were found at any point on the 



Figure 60. Hatch cover and clamps. Controlled-at- 
mosphere launching tank. 


structure, using the standard brittle whitewash 
test as the indicator. Figure 61 shows the completed 
tank suspended from the crane as it is being lowered 
in the building excavation at the time of construc- 
tion. 



40 


LABORATORY FACILITIES 



Since the tank is to be used with a photographic 
recording process, it is necessary to take special pre- 
cautions to maintain the water in excellent condition, 
eliminating anything that might decrease the light 


Figure 61. Controlled-atmosphere launching tank 
being lowered into excavation for installation. 

transmission. To assist in this matter, two corrugated 
galvanized steel storage tanks were provided for the 
clean water. Each is 14 ft in diameter by 19 ft high. 
These tanks are covered and air filters are installed 


Figure 62. Controlled-atmosphere launching tank. 
Filter with one of storage tanks in background. Vacu- 
um pump at left. 

on all openings to prevent contamination. A com- 
mercial sand filtering system is provided for use in the 
initial purifying and subsequent reconditioning of the 
pure water to be used in the tank. Figure 62 shows 
the filter with one of the storage tanks in the back- 
ground. On the left will be seen the large vacuum 


pump used for maintaining the subatmospheric pres- 
sures required for the study. 

The Launcher 

After an extensive consideration of the possible 
launcher types, it was decided to use a centrifugal 
launcher because of the compactness possible with 
this design and also because of the advantages it 
offered in obtaining accurate control of the launching 
velocity, the trajectory, and the pitch angle. It con- 
sists basically of a rotating wheel which carries a 
model chuck near its periphery. The model is pre- 
vented from spinning about the chuck axis by a 


Figure 63. Launcher mounted on open hatch cover 
with model in chuck. 

planetary system of gears mounted on the wheel and 
connected to the hub. These gears are also used for 
setting the angle of the model with respect to the 
horizontal. Figure 63 shows the launcher mounted on 
the open hatch cover with a model in place in the 
chuck. Figure 64 gives a plan view of this installation 
with the chuck empty. Figure 65 shows the opposite 
side of the launcher wheel from that seen in Figure 63. 
This view shows one of the launcher controls. The 
component parts may be readily identified by com- 
paring with the diagram of Figure 66. The launcher 
wheel is a steel plate, cadmium plated for protection 
against corrosion. It is 2}/i in. thick and, therefore, is 
heavy enough to provide sufficient fly wheel effect to 
insure very uniform velocities. The wheel is supported 
on a 4-in. stainless steel shaft which is mounted on 
four preloaded precision ball bearings running in an 
oil bath and is assembled in a quill to form an accu- 



CONTROLLED-ATMOSPHERE LAUNCHING TANK 


41 


rately aligned unit. The launcher is driven by a 10-hp 
d-c motor whose speed is controlled electronically. 
The control is activated by means of a selsyn motor 
driven by chain from the launcher shaft. The plan- 
etary gear system which prevents the rotation of the 
chuck around its -own axis is composed of specially 
cut fine-pitch precision gears. To insure maximum 
smoothness of operation and to eliminate any back- 
lash, the center gear of this train is made in three 
parts, the outer two being spring loaded against the 



Figure 64. Plan view of launcher with chuck empty. 


central section by small tangential coil springs in the 
rim. The central gear and one outer one mate with 
the hub gear, whereas the central gear and the remain- 
ing outer one mate with the chuck gear. Of course the 
hub and the chuck gear have the same diameter. The 
hub gear is mounted rigidly to the pitch-angle arm. 
This, in turn, is mounted on and rotates with the 
trajectory-angle arm which is integral with the re- 
lease arm. The trajectory-angle arm clamps to the 
trajectory scale and has a 90-degree adjustment. The 
pitch-angle arm can be adjusted to ± 10 degrees with 
respect to the trajectory-angle arm. Thus rotation of 
the trajectory-angle arm rotates both the hub gear 
and the release arm. The model chuck carries a trip 
lever which projects from its axis on the control side. 
The release arm carries a solenoid-operated release. 
In the normal position the striker finger of this re- 
lease clears the trip lever of the chuck. When the 
solenoid is energized, the striker finger moves radi- 
ally inward to a position which allows it to strike the 


trip lever on the next revolution. This releases the 
model. The working of these controls may be seen 
from consideration of the following example. Assume 
that it is desired to launch the model at a trajectory 
angle of 15 degrees to the horizontal with the model 
having a 2-degree down pitch. Assume that both 
the pitch-angle arm and the trajectory-angle arm are 
set to zero on their respective scales, and that the 
model is clamped in the chuck. It will be seen that 
under these conditions the model will be horizontal 
for any position of the launcher wheel. First, the 
trajectory-angle arm is undamped and rotated until 
its index is at 15 degrees. This rotates the hub gear 
15 degrees which causes the chuck and model to ro- 
tate the same amount. The direction of rotation is 
such that the model is now tilted with the nose down- 
ward 15 degrees from the horizontal. Careful obser- 



Figure 65. Launcher wheel from side opposite to that 
shown in Figure 63. Controlled-atmosphere launching 
tank. 

vation will show that the release arm is now in such a 
position that the striker finger will trip the chuck so 
that the gear will release and free the model at the 
exact instant the chuck centerline is 15 degrees from 
its bottom position. Next the pitch-angle indicator is 
set at 2 degrees down. This rotates the hub gear, and 
consequently the chuck and model, 2 degrees more, 
but does not move the release arm. It will now be seen 
that when the release is operated, the model will leave 
the launcher at a downward angle of 15 degrees to the 


(irrTgT oKN liAi. 



42 


LABORATORY FACILITIES 



Figure 66. Launcher controls. Controlled-atmosphere launching tank. 


horizontal and the model axis will have a 2-degree 
down pitch with respect to this trajectory. 

The model chuck was designed with great care to 
insure accurate launchings. The detail of this con- 
struction may be seen in Figure 67. It consists 
basically of a support conforming exactly to the di- 
ameter of the model and covering the 135 degrees on 
the inside of the wheel or the upper side of the tra- 
jectory. It will be seen that at the instant of release 
the chuck seat and the model have exactly the same 
motion and subsequently the chuck lifts slowly away 
from the model without disturbing it. This seat is 
made as rigid and stiff as possible in order to store the 
minimum amount of energy which might affect the 
motion of the model at the instant of tripping. The 
model is held in the chuck by means of a finger. This 
finger falls away from the model at the instant of 
tripping, under the acceleration of a very stiff spring. 
The design is such that the finger always moves faster 
than the model and thus never interferes with it after 
the instant of release. The model is placed in the 
chuck with its center of gravity at the center of the 
seat. All the rotating parts of the launcher are dy- 


namically balanced to insure vibration-free opera- 
tion. The model itself is counterbalanced by means of 
an adjustable weight located in the plane of rotation 
of the model. No provision has been made to change 
the balance of the launcher after the release of the 
model because it has been determined experimentally 
that the entire structure is so massive and rigid that 
this unbalance causes no trouble for the short periods 
that the launcher remains rotating after the model 
has been tripped. Figure 68 shows a view of the chuck 
mechanism with the model clamped in position. 

To determine the launching point or trajectory 
angle a photocell is used. A small polished stainless 
steel mirror is mounted on the launcher wheel and 
the photocell carried on the arm of the launcher 
tripper. A condenser discharging into a solenoid lifts 
the tripper into position to operate the launcher, 
the entire action taking under 4 msec. 

Trajectory Recording System 

The trajectory recording system is composed of a 
battery of synchronized high-speed motion picture 


CONTROLLED-ATMOSPHERE LAUNCHING TANK 


43 


cameras using standard 35-mm film. These cameras 
may be divided into two groups. The main battery is 
for the purpose of recording the underwater trajec- 
tory. It is made up of five cameras installed in a hori- 
zontal line along the 6-ft cylindrical tank. Two 
auxiliary cameras are used for recording the air-flight 
trajectory from the launcher to the water surface. 
These are installed in the proper two of the three 
camera windows provided above the water level in 
the main tank. A choice of location is provided for 



Figure 67. Model chuck. Controlled-atmosphere 
launching tank. 

these air-flight cameras because their field of view is 
limited by the fact that they are of necessity so much 
closer to the plane of launching. If low-angle launch- 
ings are to be studied, the cameras are placed at the 
center and the right-hand windows. If high-angle or 
vertical launchings are to be investigated, the cam- 
eras are placed at the center and the left-hand 
windows. Figure 58 shows the installation of these 
two batteries with the air-trajectory cameras in- 
stalled for a low-angle launching. The cameras them- 
selves are not visible in this picture because they are 
obstructed by the large vertical film magazines that 
are attached to the back of each camera. 

The optical coverage of the underwater bank of 
cameras is shown in Figure 69. It will be seen that at 
the plane of launching the adjacent camera fields 
have a 60 per cent overlap. In the vertical direction 
the field of view covers the entire water depth. This 
coverage means that every point in the entire under- 
water space in front of the intersection of the ad- 


jacent fields of view is seen by two or more cameras. 
The purpose of this multiple coverage is to make it 
possible to use stereoscopic technique for the analysis 
of the recorded data. Difficulty was experienced in 
designing the system so as to get the desired coverage 
without the use of a prohibitive number of cameras. 
This difficulty was solved in part by the provision of 
the 6-ft diameter cylinder which increased the dis- 
tance from the camera to the plane of launching, and 
hence increased the width of the field. However, even 
this was insufficient to permit the coverage of the en- 
tire underwater space with one line of cameras when 
equipped with the widest-angle lenses available. The 
reason for this was that the angular width of the field 
of view was substantially reduced by the refraction 
experienced by the light in passing from the air to the 
water. This reduction in field was finally eliminated 
by the use of spherical windows in front of each 
camera. The installation was carefully designed so as 
to put the front nodal point of the lens at the radius 



Figure 68. Controlled-atmosphere launching tank 
chuck mechanism with model clamped in position. 

of curvature of the window. The effect of such a 
system is to permit each light ray to pass through the 
interface at an angle of 90 degrees and thus suffer no 
refraction. These spherical windows are in effect addi- 
tional lenses. They were, therefore, made of optical 
glass, ground and polished to optical standards. Care 
was taken to insure that the inner and outer surfaces 
were concentric. The auxiliary effect of this spherical 
window in contact with the water is that the ap- 
parent distance from the camera lens to the pro- 




44 


LABORATORY FACILITIES 



jectile is greatly reduced, thus making necessary a 
very different focal setting of the lens from that 
which would have been used with a plane window. 
Careful computations were made to determine the 
optical distortions that might result from such an 
unconventional system using the design character- 
istics of the lens itself, which is a / 2.3 one-inch focal 
length Bausch and Lomb Baltar. These computations 
show that the optical characteristics for the under- 
water use would be at least as good as those of the 
lens alone in air, and in one or two characteristics, 
even better performance could be anticipated. 

The design requirement of a maximum speed of 
3,000 exposures per second imposed some very severe 
conditions on the photographic recording system. 
Such speed requires a continuous motion of the film 
as it is obviously impossible to stop the film 3,000 
times per second. Two techniques have been de- 
veloped for taking satisfactory motion pictures with 
a continuously moving film. The first one, which has 
several variations, is the introduction of some optical 
device to cause the image to move at the speed of the 
film during the exposure. The second one discards the 
conventional continuous illumination and substitutes 
in its place high-intensity flashing lights which act 
both as a source of illumination and as a camera 


shutter. It will be recognized immediately that the 
success of the second system depends upon the pro- 
curement of a high-intensity light source whose 
flashes are of such short duration that the amount of 
movement of the image on the film during exposure 
is negligible. The only variation of the first method 
that could be applied to this recording system would 
require the insertion of a rotating prism or a rotating 
bank of mirrors in the light path between the lens and 
the film. The necessity for the use of short-focus, 
wide-angle lenses makes it impossible to apply this 
method simply because there is not space available 
between the lens and the film for the rotating system. 
Therefore, it was decided to adopt the high-speed 
flash illumination technique with the resulting sim- 
plified camera design. Figure 70 shows a simplified 
drawing of the camera and magazine mounted on the 
tank window flange with the spherical window in 
place. Due to the high speed required, it was decided 
to eliminate all sliding contact between the film and 
the camera, using only rollers for guides. This made 
it necessary to design a special roller-type gate to 
insure that the film would travel exactly in the focal 
plane during the exposure. Calculations showed that 
a final speed of 30 fps would be required, even after 
due allowance had been made for a very appreciable 


CONTROLLED-ATMOSPHERE LAUNCHING TANK 


45 


overlap of successive exposures. The requirements 
for the analysis of the film record indicated that it 
would be very desirable for the film to have a con- 
stant velocity during the recording. To obtain this 
with a conventional magazine using a supply and a 
take-up spool would be very difficult and also waste- 
ful of film since such speeds would require a con- 
siderable acceleration time before the film would be 
up to speed. It was therefore decided to employ a 
special magazine so constructed that the required 
length of film could be spliced into an endless belt 
and laced over a series of rollers. This system would 
permit bringing the film up slowly to the exact speed 
required for the recording without danger of damag- 
ing the film during either the accelerating or decel- 
erating periods. Figure 71 shows the rear elevation of 
one of these magazines with the cover removed so 
that the method of lacing of the endless belt of film 
is seen. Figure 72 is a similar view from the front 


showing the camera in place on the magazine. Figure 
73 shows the assembly with the cover in place. 

The cameras are all driven by a single motor by 
means of a continuous line shaft which is directly 
connected to each drive sprocket. Figure 74 shows 
the underwater battery in place on the side of the 
tank with the drive motor at the left and the drive 
shaft running inside of its guard just below the o-b 
servation window. Figure 75 shows a close-up of the 
camera drive motor. This motor drive is a very 
special installation designed to meet the peculiar 
needs of this camera system. In the first place, it is 
desired to synchronize the speed of the film with the 
speed of the light flashes to allow for projection and 
observation of the records as motion pictures. A 
synchronous motor is therefore used. An inverter 
unit has been designed to drive the motor. The in- 
verter will operate at 62.5 cycles per second, and will 
be controlled by the laboratory constant-frequency 



Figure 70. Drawing of high-speed camera and magazine mounted on tank window flange with spherical window in 
place. Controlled-atmosphere launching tank. 




46 


LABORATORY FACILITIES 


set which will also control the flash rate of the lamp 
battery. With this combined operation, flash rates of 
3,000, 1,500, 1,000, and 500 per second will corre- 
spond respectively to 6, 3, 2, and 1 exposures per 
standard frame on the film. The inverter will 



Figure 71. Rear of high-speed camera magazine with 
cover removed. Controlled-atmosphere launching 
tank. 


deliver 1 kw of three-phase power. The motor is of 
the slotted rotor type and will deliver 1 hp at syn- 
chronous speed. To avoid damage to the film it is 
necessary to have smooth acceleration and decelera- 
tion over the entire speed range. To accomplish this 
with the synchronous motor, the motor frame is 
mounted on ball bearings so that it can rotate freely. 
The power is carried to it through a set of three slip 


rings mounted on the outside of the frame. Two 
magnetic brakes are installed, one on each end of the 
motor. The brake drum of one is mounted on the 
motor shaft and that of the other on the motor 
frame. Before the motor is started the shaft brake is 
clamped and the frame brake is loosened. The power 
is then applied and the motor starts by revolving the 
frame, with the armature and consequently the shaft 



Figure 72. Front view of high-speed camera and 
magazine with cover removed. Controlled-atmosphere 
launching tank. 


and film drive standing still. The motor is brought up 
to speed and synchronized in this condition. When 
this is accomplished, the shaft brake is released. The 
frame brake is then applied gradually, thus decelerat- 



CONTROLLED-ATMOSPHERE LAUNCHING TANK 


47 


ing the frame and accelerating the film drive. When 
the frame is brought to a complete stop, the film 
drive is, of course, operating at a synchronous speed. 
The reversal of this procedure permits controlled de- 
celeration as well. The torque applied to the frame 
brake can be varied at will to produce any rate of 
acceleration and deceleration for the film mechanism. 

In order to permit the daylight loading of the 
magazines, a foot or two of the film on each side of 



Figure 73. Camera and magazine with cover in place. 
Controlled-atmosphere launching tank. 


the splice must be exposed to the light. It would ob- 
viously be undesirable to have this portion of the 
film pass through the camera during the actual re- 
cording period. Therefore, provisions have been in- 
corporated in the drive to synchronize the film travel 
with the instant of launching. To do this for all of the 
cameras simultaneously required that each endless 
film belt should be exactly the same length, i.e., have 
the same number of sprocket holes. This is made 


possible by the use of a magazine loader which con- 
sists of a film supply spool, a take-up spool, a splicer, 
and a precision footage counter. This is shown in 
Figure 76 as it appears mounted on the magazine in 
readiness for the reloading cycle. This cycle consists 
in breaking the film belt at the original splice, splic- 



Figure 74, Underwater camera battery and motor. 
Controlled-atmosphere launching tank. 


ing one end of this break to the film going to the take- 
up spool and the other end to that of the unexposed 
film coming from the supply spool. The light-tight 
lid is then closed and a measured amount of un- 
exposed film is fed into the magazine while the ex- 
posed film is wound on the take-up spool. When the 
footage indicator shows the right amount, the door 
is opened and the film is spliced at the indicated 
sprocket holes after cutting the connections to the 
supply and take-up spools. The magazine is then 



Figure 75. Close-up view of camera drive motor. 
Controlled-atmosphere launching tank. 


ready for loading the camera. The cameras are all 
loaded with the film splice in the same position within 
a few sprocket holes. This insures that all of the 
splices pass through the camera at the same time. A 
counting mechanism is incorporated in the camera 
motor drive. This is used to give a signal at the time 



48 


LABORATORY FACILITIES 


that the film splices and the exposed film pass through 
the focal plane of the camera. This signal is electric- 
ally interlocked with the circuit which energizes the 
launcher release mechanism in such a way that the 
release mechanism can be operated only immediately 
after the splice in the exposed portion of the film has 
passed into the camera, thus insuring that the entire 
length of usable film is available for recording the 
launching. It is possible that at certain launching 
speeds the launcher and the film drive would be so 
synchronized that the model would never be in the 
correct position for launching during the short period 



Figure 76. Magazine loader for high-speed cameras. 
Controlled-atmosphere launching tank. 


that the film splice position indicator permits launch- 
ing to take place. To take care of these cases a small 
worm gear is provided on the film drive motor by 
means of which the motor frame can be rotated, thus 
changing the phase relationship between the film and 
the launcher. This mechanism can be seen at the 
extreme right of the motor shown in Figure 75. 

It will be seen that about 250 ft of film are exposed 
by the camera battery of the recording system for 
each launching. An organized test program could be 
expected to produce several thousand feet of film per 
day. The necessity for rapid means of processing this 
film under conditions to produce the maximum den- 
sity with the minimum grain size was the determin- 
ing factor in the decision to install the continuous 
film processing equipment described in Section 
2.6. This machine was designed to process from 400 
to 1,000 ft of film per hour, depending upon the de- 
tails of the developing cycle required. 

Light Source. As previously indicated, the success- 
ful operation of this recording system is dependent 
upon the use of high-intensity flashing light sources 
of extremely short flash duration. A simple computa- 


tion of the speed of the film and the projection ratio 
required for analysis showed that the maximum ap- 
plicable effective flash* duration would be between 1 
and 2 /xsec if sufficiently sharp film images to give 
the required accuracy of measurement were to be ob- 
tained. This means that extremely high light inten- 
sity and quantity would be required to illuminate the 
test space sufficiently to obtain satisfactory records. 
This condition is aggravated by the fact that for 
these extremely short exposures, the photographic 
law of reciprocity seems to break down. For all 
normal ranges of photographic work satisfactory film 
exposures can be obtained if the product of the light 
intensity times the time of exposure is kept constant. 
This in itself is a severe requirement which can easily 
be seen from the consideration of an example. The 
normal high-speed motion picture camera takes 
pictures at the rate of about 64 frames per second for 
‘‘slow motion” shots. With a good shutter this results 



Figure 77. Special reflector for light source lamp. 
Controlled-atmosphere launching tank. 


in the exposure time of approximately 0.01 sec. If in- 
stead of 0.01 sec, exposure flash illumination is used 
for a flash duration of 2 /zsec, the reciprocity law 
would require an illumination of 5,000 times the in- 
tensity to secure a film image of the same density. 
However, experiment has shown that an increase in 
the light intensity by a factor of 5,000 does not give 
satisfactory exposures. The intensity must be in- 
creased to several times this amount for good work. 

A consideration of these requirements, together 
with the characteristics of existing flash lamps, indi- 
cated that a multiple battery of synchronized lamps 


CONTROLLED-ATMOSPHERE LAUNCHING TANK 


49 


would be required since there was little or no possi- 
bility of obtaining a single light source of sufficient 
intensity having such a short flash duration. The 
assistance of Harold Edgerton and his group of co- 



Figure 78. Four-unit 
light battery, rear view. 
Controlled - atmosphere 
launching tank. 


Figure 79. Four-unit 
battery, front and side 
views. Controlled-atmos- 
phere launching tank. 


workers at the Massachusetts Institute of Tech- 
nology was enlisted because of his wide experience in 
the development and use of flash lamps. The system, 
consists of a battery of from 30 to 42 flash lamps, all 
operated in synchronism during the recording period. 
Measurements indicate that the individual lamps are 
synchronized with each other within less than 34 Msec. 

Each lamp consists of a straight quartz tube about 
8 in. long mounted at the focal point of a special 
cylindrical reflector. The cross section of this reflector 
is approximately ellipsoidal. The exact contours were 
calculated to provide the best illumination possible 
over the test area. The shape of this reflector was de- 
signed by I. S. Bowen, a member of the Physics De- 



Figure 80. Batteries of lights installed. View from 
inside tank. Controlled-atmosphere launching tank. 

partment of the California Institute of Technology. 
Figure 77 is a photograph of one of these reflectors. 
It is constructed of Lucite. The reflecting surface is 
aluminized by the standard sputtering technique. 
These lamps are assembled in batteries of four or 
more, as can be seen in Figures 78 and 79. Figure 78 
shows the rear view of a battery. The ends of the 
quartz tubes and the electrical connections may be 
seen inside of the Lucite guards which house them. 
These guards are necessary because the glass-to- 
metal seals of the tubes are very fragile. The lamps 
are installed in the longitudinal Lucite tubes travers- 
ing the launching tank. Figure 80 shows thirty lamps 
installed in batteries of six in five of the tubes. This 
photograph was taken inside of the launching tank 
and also shows the heavy 2x1 2-in. vertical columns 
that carry the hoop stress across the opening at the 
intersection of the two longitudinal cylinders making 






50 


LABORATORY FACILITIES 


up the tank. Three of the spherical camera windows 
are seen along the horizontal centerline of the picture. 

The power for the operation of each light is carried 
through an individual coaxial cable running from the 
light to the control panel. Each light is operated 
through an individual surge circuit which receives 
power from a large d-c power source. The power source 
operates at from 3 to 5,000 volts and the lights 
operate at twice this value through a voltage doubler 
incorporated in the circuit. The power consumption 
of each light is approximately 0.8 joules per flash. 
Thus, at 3,000 flashes per second, the battery of 
thirty lamps requires a continuous input of approxi- 
mately 80 kw. It must be remembered that at this 
speed the lights are lit only about V 200 of the time. 
This means that the power input during the period of 
illumination is at the rate of better than 16,000 kw. 
The heat generated in the tubes themselves limits the 
length of operation since the tubes get quite hot and will 
collapse if they are operated too long. At flash rates of 
1 ,000 per second and above, the only significant heat 


dissipation is through radiation. Experiments have 
shown that 3,600 flashes per run are the maximum 
that can be employed for successful high-speed 
operation. At flash speeds of a few hundred, however, 
the average energy input becomes low enough so that 
conduction contributes a significant amount to the 
total energy dissipation. For such speeds the number 
of flashes per run can be increased and at flash speeds 
of 100 or 200 per second, the energy is dissipated 
rapidly enough to permit of continuous operation. 

Spectroscopic analysis of the light shows it to be 
composed of discrete lines. Most of the energy lies 
between 4,000 and 4,600, which coincides with the 
wavelength at which the transparency of water is the 
greatest. 

Figure 81 shows a final sketch of the tank with 
portions cut away to make it possible to see the inter- 
relationship of the launcher, the air camera, the 
underwater camera bank, and the flash lamps. The 
central control station for the launching tank is lo- 
cated on the basement floor south of the tank. From 



Figure 81. Cut-away drawing showing interrelation of parts. Controlled-atmosphere launching tank. 


CONTROLLED-ATMOSPHERE LAUNCHING TANK 


51 



Figure 82. Line diagram of analyzer system. Controlled-atmosphere launching tank. 


this point the launcher may be started or stopped 
and its speed set. The camera drive motor may be 
controlled, and the high-voltage power supply turned 
off and on. Also the vacuum pump and valve controls 
for adjusting the pressure within the tank are located 
here. An automatic interlock sequence prevents a 
launching from being made until all the accessories 
necessary to record the trajectory are in operating 
condition. When everything is in order, an indicating 
lamp shows that a launching can be made. When the 
launching control is actuated, the operation of all the 
equipment is fully automatic. 

Analyzer System 

Details of the analyzer system are not available 
because it is only in the initial stages of design and 
construction. However, the general lines of the de- 
velopment have been established and will be dis- 
cussed. The basic principle of the analyzer essentially 
duplicates that of the recording system. Projectors 
will take the place of the cameras and a movable 
screen will replace the tank and the model. All of the 
films from one run of the recorder will be placed in the 
corresponding projectors with the film strips synchro- 
nized so that the corresponding frames taken at the 


same time will be projected at the same time. The 
film drive of the projectors will be a continuous shaft 
so that once the film strips are synchronized, they 
will remain so during the projection of the entire run. 
Figure 82 shows a line diagram of the analyzer sys- 
tem. It represents a point on the trajectory in which 
the projectile was in the field of view of cameras No. 2 
and 3 so that projectors No. 2 and 3 are projecting the 
two images into the analyzer space. It is obvious that 
there is only one position in this space in which the 
two images will coincide. The exploring screen of the 
analyzer is then maneuvered into such a position that 
the two images both show on it. Additional maneu- 
vering will bring the screen into such a position that 
the images fuse into one. This will require move- 
ments in three linear directions and also in pitch and 
yaw. These movements will be transferred to a bat- 
tery of counters. When the screen is finally in the 
exact position required for the precise fusing of the 
images, then the counters will record the position of 
the projectile in space. It is planned to build the 
analyzer to a scale of one-half that of the recording 
equipment. 

The projectors for this analyzer will have to be 
precision instruments. As a first step in their con- 
struction, lenses were procured in matched pairs at 


AiONKmfcNTllO 


52 


LABORATORY FACILITIES 


the time the cameras were constructed. One lens of 
the matched pair is to be used in the camera and the 
other lens in the corresponding projector. The gate 
mechanism will be designed to hold the film in the 
exact focal plane corresponding to that used in the 
camera. The light source will be kept at as low an 
intensity as is consistent with the required accuracy of 
the readings in order to reduce heat which might 
affect both the dimensions of the film and of the 
optical system. The temperature will be controlled 
further by the employment of water cells and individ- 
ual air cooling. In order to check the location of each 
frame, it is planned to install a series of reference 
marks on the rear wall of the launching tank. These 
marks will be reproduced on a background screen at 
the rear of the analyzer, and before making a meas- 
urement, a check will be made to see that the image 
of the marks from the films in the projector fall on the 
corresponding marks on this screen. The exploring 
screen is designed to be mounted on a carriage sus- 
pended from longitudinal rails. This longitudinal 
carriage will, in turn, provide a set of transverse rails 
upon which will run the screen mount. The trans- 
verse carriage will carry an inverted pedestal which 
will provide the required vertical movement. The 
screen will be mounted on the lower end of the 
pedestal stem through a system which will provide 
the final pitch and yaw motions. Selsyn repeaters will 
be used as position indicators to transmit the re- 
quired information to the operator’s desk. 

2 5 FREE-SURFACE WATER TUNNEL 

The purpose behind the construction of the free- 
surface water tunnel was explained in Chapter 1. In 
general plan and in contemplated operation it is very 
similar to the main high-speed water tunnel. That is, 
it has a closed-circuit circulation system which is 
driven by a propeller pump powered by a variable- 
speed d-c motor. The circuit is arranged in a vertical 
plane with the working section in the upper hori- 
zontal run. The design specifications differ consider- 
ably from those of the high-speed water tunnel in that 
a much larger working section is to be provided. The 
cross section of the water jet is 20 in. square, which 
gives a cross section that is just under 3 sq ft as com- 
pared to the 1 sq ft of the high-speed water tunnel. 
It will be noted that the flow is square instead of 
circular in cross section. This is necessary to provide 
for the free surface of the jet in the working section 
which is the main distinguishing feature of this piece 


of apparatus. The tunnel is designed to operate at 
velocities up to 25 fps. The exact maximum velocity 
will depend upon the equilibrium reached between 
the power available in the motor drive and the fric- 
tion losses in the circuit. The tunnel is designed to 
permit the operation of the working section at con- 
trolled pressures. Since the jet has a free surface in 
this area, it is not possible to control the pressure by 
the simple means used in the high-speed water tun- 
nel. Instead, it is necessary to control the pressure in 
the free gas space above the jet. This is done by 
connecting the tunnel to the same vacuum control 
system provided for use with the controlled-atmos- 
phere launching tank. No operation is contemplated 
at pressures above atmospheric in the working sec- 
tion. The vacuum system will provide variations in 
pressure from 1 atmosphere down to to Vis of an 
atmosphere. 

Figure 83 shows a perspective sketch of the entire 
tunnel. The observer is shown watching the operation 
of a model mounted on the balance in the working 
section. The flow is from right to left as indicated by 
the arrow. From the working section the jet passes 
into a closed section which leads directly to a series of 
vane diffusers which increase the cross section and 
decrease the velocity in a series of four steps, each of 
which has a ratio of about 2 to 1 . The flow leaves the 
last stage with a very low velocity and enters an 
especially designed air separator, the horizontal trays 
of which can be seen through the cut-away opening in 
the upper left-hand corner of the sketch. At the 
downstream end of the air separator the flow goes 
through a vane elbow which directs it vertically 
downward, and on leaving the lower level, goes 
through another vane elbow from which it enters the 
inlet of the main circulating pump. The discharge 
from the pump goes into a circular diffuser section 
which decreases the velocity. At the point of the max- 
imum diameter of the diffuser, a transition section is 
entered which gradually changes the cross section 
from round to square. This leads to a third vane el- 
bow which deflects the flow vertical!}^ upward. The 
acceleration of the flow to the working velocity be- 
gins in the vertical section above this third elbow. 
The channel section contracts in one dimension only. 
This contraction is completed by the fourth vane el- 
bow which is so designed as to produce a considerable 
acceleration. The flow leaves this vane elbow in a 
horizontal direction. It now has a rectangular cross 
section 20 in. high, which is the depth required in the 
working section, but with a full width of the main 


FREE-SURFACE WATER TUNNEL 


53 


diffuser. The final acceleration is carried out in a 
two-dimensional nozzle designed in the same careful 
manner as the one used in the high-speed water tun- 
nel to avoid any local areas of low pressure. At the 
nozzle exit the flow cross section has been reduced to 
the 20-in. square dimension of the jet in the working 
section. 

The working section is provided with Lucite win- 
dows on all faces. These are held in a comparatively 
light steel framework designed to take the stresses 
involved in the low-pressure operation. The windows 
are divided into two sections, each about 4 ft long, by 
steel columns, thus giving a total working section of 
about 8 ft. A 10-in. air space is provided over the free 
surface of the jet. The side windows are, therefore, 30 
in. high, whereas the top and bottom windows are 
only 20 in. wide. In order to eliminate deflections 
these large windows are made of very thick Lucite 
procured to laboratory specifications. The side walls 
are 4 in. in thickness and the top and bottom win- 
dows are 3 in. thick. Provisions are to be made for 
mounting balances either in the bottom panels or the 
top panels of the working section. An adjustable lip 
will be required at the end of the nozzle to provide a 
clean interface from the closed channel to the free 
surface. Likewise it is planned to install an adjust- 
able entrance vane at the downstream end of the 


working section to provide a smooth transition from 
the free-surface operation back to the closed channel. 
Many of the investigations contemplated will result 
in disturbances of the free surface which may pro- 
duce splash and spray. Provisions are made to collect 
the water thus involved which does not re-enter the 
closed channel at the lower end of the working section 
and to return it by means of a pump into the main 
circulation system. It is comtemplated that the 
standard three-component balance used in the high- 
speed water tunnel will be usable in this tunnel as 
well. However, special balances will also be required 
which will permit of a vertical adjustment of the 
model so as to allow testing at various distances be- 
low the free surface. A balance with a similar vertical 
adjustment mounted in the top window will permit 
of supporting the body under test above the free sur- 
face and of adjusting its degree of immersion to any 
desired amount. It is felt that a four-component 
balance will give sufficient flexibility for the re- 
quired measurements. Separate adjustments will be 
necessary for pitch and yaw since the effect of one 
cannot be simulated by a simple rotation of the 
model of 90 degrees from the plane in which the other 
was measured. 

Figure 84 shows a drawing of the battery of de- 
celeration vanes. It will be noted that the entry and 



Figure 83. Free-surface water tunnel. Hydrodynamics Laboratory, California Institute of Technology. 


54 


LABORATORY FACILITIES 


exit cross sections are fixed, which means that the 
o\'erall velocity reduction ratio is set independent of 
the velocity of operation of the tunnel. 


HORIZONTAL DECELERATION VANES 




Figure 84. Battery of deceleration vanes. Free-siir- 
face water tunnel. 

Design of an air separator for a system of this kind 
has presented a great many difficulties. It is contem- 
plated that a rather large amount of air will be intro- 
duced into the working section from time to time and 
this air may appear in the form of rather fine bubbles, 


many of which may be in the lower levels of the 
working section. The rate of rise of such bubbles 
is rather small. This means that either a long time or 
a short distance to a free surface is required if ade- 
quate separation is to be obtained. Although the 
velocity at which the flow leaves the battery of de- 
celeration vanes will probably be under 2 fps, the 
depth will be very great, too great to permit of the 
rise of a small bubble to the surface before the flow 
reaches the vane elbow and is directed down away 
from the free surface towards the circulating pump. 
It was, therefore, decided to divide the air separator 
section into a series of shallow channels and to pro- 
vide access along the upper surface of each channel to 
the free surface. This is accomplished by the use of a 
series of double wall trays at the upper surface of 
which is a flat plate. The lower surface is made up of 
expanding metal, thus permitting free access of any 
bubble to the space within the tray. This space con- 
nects directly with channels leading to the free sur- 
face that is continuous throughout the air separator 
section. These trays are approximately 3^ in. thick 
and are spaced with a 2-in. vertical separation which 
makes the net thickness of the flowing stream 13 ^ in. 
The average time of passage for the flow through the 
tray section for the maximum velocity of operation 
will be approximately 5 sec. This means that bubbles 
with an effective rate of rise of 3^ ips or greater will be 
separated from the flow. In order to assist this separa- 
tion, arrangements have been made to provide a 
slight pressure drop which will cause a small flow 
from the main stream up through the trays and out 
through the channels to the free surface. This flow 
will be collected in a system similar to the one used 
for taking care of the spray from the working section. 
It will then be returned to the main flow through 
another pump which injects it upstream from the air 
separator. 

It proved advantageous in the construction of the 
air separator to give a slight inclination downward in 
the direction of flow to the cylindrical case. The re- 
sult of this is that the vane elbow following the air 
spacer is slightly elliptical in cross section. Special re- 
inforcing rings were designed to take care of the 
asymmetric stresses caused by this shape when the 
tunnel is being operated at subatmospheric pressures. 
The lower vane elbow is likewise elliptical and re- 
quires the same treatment. The section is transformed 
into a circular one, however, by the time that the 
flow reaches the pump. The pump is a standard Peer- 
less 42-in. propeller pump of the same type as that 


FREE-SURFACE WATER TUNNEL 


55 



used in the high-speed water tunnel. The mechanical 
design of the bearings and shaft seal were modified, 
however, for use in the closed circuit of this type, with 
horizontal drive and with a possibility of negative 
pressures tending to cause air leaks in the seal. Al- 
though the pump is physically much larger than the 
one used for the high-speed water tunnel, and al- 
though it circulates approximately the same quantity 
of water, the head requirements of this tunnel are so 
much lower due to the low velocity in the working 
section that the power requirements are greatly re- 
duced. Therefore, the pump is driven by a 75-kw 


the details of the contours. These contours were ma- 
chined very accurately using a carefully constructed 


Figure 86. Downstream view of pump bowl, propel- 
ler in place. Free-surface water tunnel. 


Figure 85. Upstream view of pump bowl, propeller in 
place. Free-surface water tunnel. 


rectifier set which has both armature and field con- 
trols for precise speed adjustment. Figures 85 and 
86 show upstream and downstream views of the 
pump bowl with propeller in place. Figure 87 is a 
photograph of the 75-kw rectifier set. Figure 88 shows 
a photograph of the transition and third vane elbow. 
Figure 89 shows the accelerating vane elbow to 
which is bolted the two-dimensional nozzle. Special 
care was taken with the alignment of the vanes in 
both of these elbows in order to insure the proper 
direction of flow, since disturbances introduced in 
these points by improper alignment would be difficult 
to remove before the working section was reached. 
Figure 90 is a photograph of the two-dimensional 
nozzle, and Figure 91 is the working drawing showing 


Figure 87. Seventy-five-kilowatt rectifier set for free- 
surface water tunnel. 

wooden template. Both the top and bottom plane 
surfaces and the side contours were worked until 



56 


LABORATORY FACILITIES 




Figure 89. Accelerating vane elbow. Free-surface 
water tunnel. 

factor of the quality of the flow in the working section 
itself. 

The preceding description represents the present 
state of the design and construction of this tunnel. 
It will be seen that there are several design problems 


yet to be solved. Furthermore, it is anticipated that 
some minor operating difficulties will be encountered 
at the time the tunnel is put into service because 
there is little precedent available concerning the be- 
havior of the free-surface jet. With a depth of 20 in., 
the velocity of a wave on the free surface is about 
fps- Most of the operations contemplated will be 


Figure 90. Two-dimensional nozzle. Free-surface 
water tunnel. 

at velocities well above this figure. For example, at 

25 fps, there will be enough energy in the jet to pro- 
duce a hydraulic jump of appalling magnitude as 
compared to the air space in the working section. For 
this and similar reasons it is anticipated that great 
care will be necessary during the initial period while 
the laboratory staff is learning the operating char- 
acteristics of this new tool. 

26 PHOTOGRAPHIC EQUIPMENT 

2.6.1 Photographic Equipment 

and Processing Facilities 

In any research laboratory, photographic equip- 
ment is probably the most important and most used 
facility outside of the basic apparatus of the labora- 
tory itself. The specialized requirements of a hydro- 
dynamic research program call for equipment to 
record high-speed phenomena under a wide latitude 
of lighting conditions. Such equipment must include, 
in addition to specific purpose cameras like those used 
with the controlled-atmosphere launching tank, a 
variety of plate and roll film cameras and movie cam- 
eras of both normal-motion and high-speed types. 
Suitable darkroom and processing facilities are nec- 
essary to handle film and produce final prints and 
enlargements. The following paragraphs contain a 
brief description of the facilities and more important 


they were smooth and then all of the component 
parts were cadmium plated and polished. These pre- 
cautions were taken because the nozzle is the most 
critical part of the circuit as it is the determining 


Figure 88. Transition and third vane elbow. Free- 
surface water tunnel. 



PHOTOGRAPHIC EQUIPMENT 


57 


L 

W 

L 

W 

L 

W 

2 . 0 ^ 

3jOO 

4.00 

5.00 

6.00 

7.00 

8.00 

9.00 

10.00 

11.00 

12.00 

13.00 

14.00 

15.00 

16.00 

17.00 

18.00 

19.00 

20.00 
21.00 
22.00 

23.00 

24.00 

25.00 

26.00 

27.00 

28.00 

29.00 

30.00 
3 1.00 

32.00 

33.00 

SOXXX ) 

i.003 

20.02 

2a04 

20.08 

20.12 

2ai8 

20.24 

2a30 

20.36 

20.42 

20.48 
2a54 
20.62 
20.70 
20.78 

2a86 

20.94 

21.02 

21.10 

21.18 

21.26 

21.34 
21.44 
21.54 
2 1.66 
2 1.78 
21.92 
22.06 
22.20 

22.34 

22.48 
22.64 

34.00 

35.00 

36.00 

37.00 

38.00 

39.00 

40.00 

41.00 

42.00 

43.00 

44.00 

45.00 

46.00 

47.00 

48.00 

49.00 

50.00 

51.00 

52.00 

53.00 

54.00 

55.00 

56.00 

57.00 

58.00 

59.00 

6aoo 
6 1.00 

62.00 

63.00 

64.00 

65.00 

66.00 

22.82 

23.00 

23.18 
23.38 

23.60 
23.82 
24.06 
24;32 

24.58 
24.86 

25.16 

25.46 
25.78 
26.11 
26.44 
26.80 

27.18 

27.58 

28.01 

28.47 
28.96 
29.49 
30.05 
30.62 
31.20 

31.84 

32.48 
33.14 

33.84 

34.60 
35.36 

36.16 
36.98 

67.00 

68.00 

69.00 

70.00 

71.00 

72.00 

73.00 

74.00 

75.00 

76.00 

77.00 

78.00 

79.00 

8aoo 

81.00 
82.00 

83.00 

84.00 

85.00 

86.00 

87.00 

88.00 

89.00 
9aoo 

91.00 

92.00 

93.00 

94.00 

95.00 

96.00 

97.00 

37.82 

38.70 
39.60 

40.52 

41.44 

42.40 

43.40 

44.40 
45.42 

46.52 

47.70 
48.92 
5a22 
5 1.62 
53.12 
54.68 
56.26 
57.94 
59.76 
61.64 
63.36 
65.08 
66.62 
68.00 
69.16 
70.14 
70.88 

71.44 
71.80 
72.00 
72.00 



Figure 91. 


Details of contours of two-dimensional nozzle. Free-surface water tunnel. 





Figure 92. Type K-17-B aircraft camera, ‘‘A’’ in position to take pictures through side window of working section 
“B.” A view camera, “C,” is mounted above the working section to record the view from the top. The intervalo- 
meter, “D,” is resting upon the power supply, “E,’’ for the three spark lamps, “F,” used in this setup. 





58 


LABORATORY FACILITIES 


items of portable equipment available to the Hydro- 
dynamics Laboratory. 

2.6.2 Portable Camera Equipment 

The laboratory is equipped with still camera 
equipment which will meet all the demands from the 
routine copying of drawings, photographs, and printed 



Figure 93. Aircraft camera in stored position. 


matter to stopping the motion of speeding objects, 
and from photographing buildings, laboratories, and 
apparatus to recording minute imperfections in deli- 
cate instruments. In addition to a group of standard 
cameras, including all sizes and types from 35-mm 
for roll film to 8xl0-in. view type for cut film and 
plates, the laboratory has two Fairchild K-17B 
aerial cameras using 9-in. roll film. These cameras 
may be used for single pictures or, in conjunction 
with an intervalometer, to make a series of exposures 


automatically at time intervals ranging from 3 to 
120 sec. 

The lighting used with the still equipment in- 
cludes continuous illumination from photoflood, 
tungsten arc, or high-intensity mercury vapor lamps, 
or flash illumination from a General Radio Strobolux 
or from Edgerton-type short-duration flash lamps. 
(See Section 2.4.4.) 

An arrangement for making spark photographs of 
high-speed phenomena in the water tunnel is shown 
in Figure 92. For this use the aircraft camera is 
operated with the usual electric drive on the shutter 
and film wind, although this type may be operated 
manually. The camera illustrated has been modified 
so that it will discharge a group of spark lamps when 
its shutter is opened to full aperture and so that it 
will advance the film 3, 4 }/^, or 9 in. per frame. Note 
that it is kept near the working section of the water 



Figure 94. Block diagram showing electrical hookup 
for aircraft camera and spark lamp. 


tunnel and ready for immediate use. It has been 
mounted in a lightweight tubular steel framework 
which is hinged to fold upward against the wall for 
storage as shown in Figure 93. 

Frequently it is advantageous to photograph the 
same action simultaneously from two angles. This is 
being done in Figure 92, in which it will be noticed 
that a view camera has been placed above the work- 
ing section of the tunnel. The photographer holds 
the shutter of the view camera open by pulling a 
cord, then presses a switch to operate the aircraft 
camera, the shutter of which discharges the lamps. 
The block diagram. Figure 94, shows that a trigger 
switch also may be used to test the lights or to take 
pictures with the view camera when the aircraft 
camera is not in use. 

The available motion picture equipment permits 
recording a wide range of the very high-speed hydro- 
dynamic phenomena under investigation, as well as 
all the normal-speed motions encountered. The 
former is accomplished with a General Radio high- 


ly 




PHOTOGRAPHIC EQUIPMENT 


59 



Figure 95. Half-frame, high-speed motion pictures made with the General Radio camera. Sequence of exposures is 
from top to bottom and from leR to right. The pictures cover a period of approximately 1/50 second; individual expo- 
sures were less than 5 microseconds. 





60 


LABORATORY FACILITIES 




Figure 96. Photographic laboratory and studio facilities. 


speed 35-mm camera. This camera is used in con- 
junction with the Edgerton-type lamps which can be 
flashed at rates up to 3,000 times per second while 
the duration of a single spark is somewhat less than 
5 /xsec. In this camera the film moves continuously 
past a shutterless lens and over a large sprocket on 
the side of which a series of electric contacts are so 
spaced that a circuit will be completed each time the 
film has advanced one frame. The extremely bright 
spark is of such short duration that it is unnecessary 
to stop the film for each exposure and no shutter is 
needed. At 1,600 standard frames per second the film 
moves 100 fps or approximately V 200 in. during the 
flash. This is almost negligible in the majority of 
cases, but not when fine detail is desirable. By mak- 
ing pictures of the usual width but only half the 
standard frame height, the laboratory has been able 
to secure high-speed motion pictures of remarkable 


sharpness. The pictures reproduced in Figure 95 were 
obtained in this manner. 

^ ® * Darkrooms, Processing, 

and Printing Equipment 

Five darkrooms, fully equipped, are provided for 
processing film, making prints, enlargements, and 
lantern slides. A studio, a chemical mixing room, 
drying and mounting rooms, and refrigerated storage 
space for unused film complete the photographic de- 
partment. Figure 96 is a plan showing the arrange- 
ment of the rooms and the location of major items of 
equipment. 

Cut and roll films are loaded and processed in the 
developing room which is equipped with trays, six 
water-jacketed tanks, film hangers, viewing light, 
drying cabinet, and storage space for film holders and 






ELECTRICAL ACCESSORIES 


61 


film. Cut film is developed in hangers which are pro- 
vided for the various sizes including 8x10 in., and roll 
film is processed on adjustable reels. The equipment 
permits aircraft film to be handled in lengths up to 
150 ft. 

In the two darkrooms labeled ‘‘35 mm’^ and “16 
mm,” motion picture film is processed by machines 
which perform the entire operation, including drying. 
These rooms also contain equipment for loading and 
editing film and tanks for the storage of developing 
and fixing solutions. The laboratory does not have 
machines for printing motion picture positives. In 
the printing room are four printers on which contact 
prints of any size up to 11x14 in. can be made. One 
printer is designed especially for use with rolls of 
negatives from the aircraft cameras. All four are 
supplied with power at a constant voltage and with 
automatic timing devices. Prints are washed in a 
machine of the rocker type. 

The enlarging room is equipped with an autofocus 
and a precision enlarger. Negatives from 9x12 cm to 
5x7 in. can be enlarged to slightly more than four 
diameters, smaller negatives to fifteen diameters. 
Adjoining the printing and enlarging rooms is the 
drying room which houses a drum-type dryer for 
prints and the machine in which aircraft film is dried. 
This room also contains a print straightener and 
equipment used in treating prints before they are 
dried. 

In the office and mounting room there is a densito- 
meter, a safe in which negatives are stored, cabinets 
for prints and photographic notes, tables with trans- 
parent illuminated panels, and suction plates for use 
in preparing prints for the dry-mounting press. In 
addition to the usual trimming boards there is a 
paper-cutting knife for trimming prints in batches of 
100 or less. 

Provision is made in the studio for the photography 
of instruments and models. A camera stand and 
easel facilitate making copies, or photographing line 
drawings and printed material. Miscellaneous equip- 
ment includes fluorescent, spot and flood lights, 
lightstands, backgrounds, tripods, and unipods. 
The microphotographic camera is housed in the 
studio. 

A room adjoining the developing and film process- 
ing rooms is set apart for the storage of chemicals and 
the mixing of all solutions. There are scales for weigh- 
ing chemicals, graduates and pipettes for measuring 
liquids, a metering device for water, and both large 
and small mixing vessels equipped with mechanical 


stirrers. This room and all darkrooms are equipped 
with stainless steel sinks and supplied with hot, cold, 
and iced water. 

2*^ ELECTRICAL ACCESSORIES 

Most of the electrical and electronic equipment of 
the laboratory form an integral part of the main 
pieces of apparatus, and have been described in 
connection with them. However, there are a few 
general facilities that are described in the following 
paragraphs. 

The laboratory is equipped with a source of con- 
stant frequency of the quartz-crystal type. It consists 
of a 100-kilocycle GT-cut low thermal drift crystal in 
a stabilized oscillator circuit. Means are provided for 
adjusting the frequency of the oscillator to zero beat 
with WWV, the standard-frequency station of the 
National Bureau of Standards. Following the oscil- 
lator is a tripler to produce 300 kilocycles and multi- 
vibrator-type frequency dividers which provide 
3,000-cycle per second output. The 3,000-cycle per 
second signal is distributed about the laboratory. 

At the water tunnel the 3,000-cycle per second 
signal is put into a frequency dividing unit which 
puts out 100- and 120-cycle per second positive 
pulses. This pulse output is used to drive a parallel 
inverter of the thyratron type at either 50 or 60 cycles 
per second. The inverter can feed a 500-watt load, 
and is used to power the synchronous motor that 
provides the standard for control of dynamometer 
speed. The inverter may be used to drive any small 
timer of the synchronous motor type anywhere in the 
laboratory whenever greater precision of timing 
than is available from the power lines is desired. 

At the launching tank the 3,000-cycle per second 
signal from the constant-frequency set is run into a 
set of frequency divider and pulse generators which 
provide positive pulses at 3,000, 1,500, 1,000, and 500 
cycles per second for operation of the stroboscopic 
lights. The inverter which supplies power to the 
synchronous motor driving the cameras is also driven 
from the same 3,000-cycle per second constant-fre- 
quency source. 

The laboratory has available a frequency changer 
capable of supplying “high-cycle” power. The fre- 
quency range of the machine is 0 to 300 cycles per 
second at 1.22 volts per cycle. A maximum of 7.5 kw 
may be delivered to a suitable load. One use of this 
machine is to power the motors driving the propellers 
of water tunnel models. 



62 


LABORATORY FACILITIES 


For the operation of special equipment requiring a 
d-c power source, 24 volts direct current is provided 
throughout the laboratory. This makes it possible to 
use a 14-channel recording oscillograph (Consoli- 
dated 5-101) anywhere in the building. 

As indicated in the description of the free-surface 
water tunnel, the laboratory has a high-voltage 
power supply for the operation of the high-speed, 
high-intensity flash lamps. This power supply is of 
the rectifier type, and operates over a range of from 
4 to 12 kw. Its maximum output is 100 kw. Arrange- 
ments are being made to provide utility and control 
facilities together with the necessary power lines, to 
make it possible to utilize this power at each of the 
major pieces of equipment to operate banks of flash 
lamps and to take high-speed motion pictures. 

A small shop is available for the maintenance of the 
electrical and electronic equipment, and for the con- 
struction of the special apparatus required for the 
project. This shop is provided with the necessary 
tools and instruments for carrying on this work. 

2 8 SOUND-MEASURING EQUIPMENT 

The development of acoustically operated hom- 
ing projectiles has required a knowledge of the 
various self-induced supersonic noises. Cavitation 
is one of the important causes of such high-fre- 
quency noise, and the laboratory is equipped to 
measure the intensity and frequency distribution of 
sounds from this source. Design details of the equip- 
ment described in the following paragraphs will be 
found in the reports. Submerged bodies are subjected 
to cavitating conditions and the resultant noise in 
various bands from 1 to 160 kilocycles can be meas- 
ured by hydrophone units located either inside or 
outside the bodies. Such measurements are possible, 
because, although the water tunnel itself produces 
high noise levels, it is relatively “quiet” in the range 
above 6 kilocycles. Background levels in the high- 
frequency range are so low as to introduce errors of 
only a few per cent. 

^ ^ Receiving Equipment 

Two arrangements are used for receiving the noise 
emitted by cavitating projectiles. In one a crystal 
hydrophone receiver is mounted external to the water 
tunnel and is focused through a window toward the 
cavitating zone by means of a suitable reflector or 
“mirror.” This system eliminates possible disturb- 


ance to the flow and accompanying extraneous noise 
which a submerged hydrophone housing would cause. 
In the other, a receiver is mounted inside the 2-in. 
diameter projectile model itself. 

Hydrophones 


Brush Development Company type Cll-Al and 
AX90 crystal hydrophones are used. These sensitive 
units are of very small size and can be adapted with 



Figure 97. Ellipsoidal reflector and Cll-A hydro- 
phone assembled in water tank at working section 
window. Noise coming through Lucite window is 
brought to focus in the hydrophone crystal. 

few changes to installation inside the small models 
and to use with the focusing reflectors described 
below. 

Method of Assembly 

In the arrangement with the receiving system ex- 
ternal to the tunnel, the hydrophone is placed at the 
focal point of spherical or ellipsoidal reflectors and 
the assembly submerged in a water-filled tank 
attached to the side of the working section. Figures 




ELECTRICAL ACCESSORIES 


63 


97 and 98 show the installation with an ellipsoidal 
reflector focused to pick up noise from a model 
(whose tip can be seen projecting past the reflector 
in Figure 98). The noise originating from cavitation 
on or near the projectile surface is transmitted 
through a water medium continuous, except for the 
Lucite window, to the reflecting surface and back to 
the hydrophone. The setup is spaced so that the 
hydrophone is at one focal point of an imaginary 
ellipsoid of revolution and the cavitation is at the 
other. Provisions are made for focusing from any 



Figure 98. Hydrophone-reflector assembly focused 
to receive noise from cavitation on projectile surface. 
Note that assembly can be positioned at any point 
within the external water tank. 


and Cl and C 2 are the velocities of sound in mediums 
1 and 2. 

The greater the difference between the products 
pc, the greater will be the reflection. Consequently, 
to obtain good reflection of sound traveling at high 
velocity in a dense medium, the reflector should be a 



position inside the exterior tank. The focusing helps 
isolate the source of noise and concentrates more of 
the total sound energy at the hydrophone. 

Sound Reflectors 

Three sizes of ellipsoidal mirrors are available. 
Each has a focus-to-focus distance of 16.2 in. The 
aperture diameters are 10, 5, and 3 in., respectively. 
These are shown in Figures 99 A, B, and C. A single 
spherical mirror with a 10-in. aperture is also avail- 
able. This is shown in Figure 100. 

The mirror construction is based on the fact that 
the reflection of sound takes place when the waves 
strike a discontinuity in the transmitting medium. 
The per cent of the incident sound pressure which is 
reflected is the ratio 

Pi Cl — P2C2 
Pi Cl -|- p 2 C2 ’ 

where pi and P 2 are the densities of mediums 1 and 2, 



Figure 99A, B, C. Ellipsoidal reflectors with aper- 
tures of 10, 5, and 3 in. 

surface which forms a boundary with a low density 
substance in which sound travels slowly. The re- 
flectors just described use air as the medium at the 
reflecting surface. In the ellipsoidal construction two 
concentric copper shells are separated by an air 
pocket. The face of the aluminum spherical reflector 
is covered with a ^-in. thick layer of sponge rubber 
with nonintercommunicating air pockets. 




64 


LABORATORY FACILITIES 


Internal Receivers 


Free-Field Calibrations 


For mounting within the model, the AX90 hydro- 
phone is used. This unit is without integral pre- 
amplifier and requires less space than the Cll-Al 
unit. For this installation, the models are made up of 
0.020-in. wall aluminum shells. 

In addition to commercial hydrophones, one spe- 
cial receiver was constructed with ammonium di- 



Figure 100. Face view of spherical surface reflector. 
Note surface covering of sponge rubber with noninter- 
communicating air cells. 


hydrogen phosphate crystals cemented directly on to 
the inside surface of a 0.020-in. wall aluminum nose.*^ 
The X-ray photograph of Figure 101 shows the cry- 
stal locations. Four crystals are mounted on the inner 
surface of the nose at 34-in. intervals in a line parallel 
to the projectile axis. Another crystal is cemented in 
place at 90 degrees around the circumference of the 
shell. This unit is designed for an investigation of the 
location of the source of noise for various stages of 
cavitation on the hemisphere nose. 


The crystals in this model were cut and mounted at the 
Underwater Sound Laboratory of the University of California, 
Division of War Research, at San Diego. 


Equipment is available for determining free-field 
directivity patterns and frequency-response calibra- 
tion curves of the hydrophones and hydrophone- 
mirror assemblies. For these calibrations, the AX90 
hydrophone is used as a projector. It acts as an ap- 
proximate point source, because of its small physical 
size. The geometrical arrangement between source 
and receiver used in the actual water tunnel measure- 
ments are duplicated. Thus, for the ellipsoidal re- 
flectors, the two crystal units are separated by the 
distance between the conjugate foci of the ellipsoid 
shape. For these tests a rig consisting of holders for 



Figure 101. X-ray photograph of crystal pickups ce- 
mented to inside surface of aluminum nose. 

the projecting and receiving units with provision for 
rotating the projector in a circle whose center is at 
the receiving crystal is submerged to a 20-ft depth in 
a large reservoir (Morris Dam). 

Figure 102 shows the rig arranged for calibration in 
a plane normal to the receiving hydrophone stem. By 
rotating the hydrophone and mirror with respect to 
its support, calibrations can be obtained in other 
planes, for example, at 90 degrees, as shown in 
Figure 103. Examples of the directivity patterns and 
calibrations obtained with this equipment are shown 
in Chapter 7. 

Amplifying and Filtering Equipment 

Two amplifying systems are in use. One is a unit 
specially constructed in the laboratory. The other is a 
modified Naval Ordnance Laboratory Mark 3 Acous- 
tical Unit. 




ELECTRICAL ACCESSORIES 


65 


The laboratory-built equipment is designed to 
amplify the output of a detecting hydrophone in 
selected frequency ranges between 1 and 100 kc and 
to indicate the amplified voltage on a meter. With 
this unit a voltage gain of 90 db can be obtained with 
no variation over the range of 20 to 100 kc. The gain 
is adjusted with attenuator pads, having a total of 
100 db in steps of 1 db. Two sets of filters are in- 
cluded to analyze the noise spectrum. One is a high- 



Figure 102, View in aperture of 10-in. ellipsoidal 
reflector as assembled for field calibration. The AX-90 
hydrophone in foreground is used as a source and 
rotated in a plane normal to the receiving hydrophone 
stem. 

pass type with optional cutoff frequencies of 1, 5, 10, 
20, 30, 40, 60, 80, and 100 kc. The other is a low-pass 
type with the same optional cutoff frequencies. With 
this arrangement channels of different widths and 
boundary frequencies can be chosen. The actual sound 
pressure in dynes per square centimeter is propor- 
tional to the voltage recorded. The block diagram of 
the equipment is shown in Figure 104. Photographs 
of the racked units are shown in Figure 105. 

The Mark 3 equipment includes a hydrophone pre- 
amplifier and four other amplifiers to analyze the 
spectrum of the input signal over the range of 10 to 


160 kc. Each amplifier is equipped with an attenuator 
with a range of 50 db in 10-db steps. All the amplifiers 
have flat response from 10 to 160 kc. The filters in 
this equipment separate the input into four octaves : 
10 to 20 kc, 20 to 40 kc, 40 to 80 kc, and 80 to 160 kc. 
Each amplifier drives an Esterline Angus graphical 



Figure 103. Same as Figure 102 but assembled at 90 
degrees for calibration in a plane containing the receiv- 
ing hydrophone stem. 


recorder, so a continuous record of all four octaves 
can be kept. The gain of each amplifier is about 80 
db. Front- and rear-view photographs of this equip- 
ment are shown in Figure 106. 


PREAMPLIFIER 


1 nUl-OAO« 


ATTENUATORS 



Figure 104. Block diagram of laboratory noise meas- 
uring system. 


For calibration of either amplifier system a known 
voltage is inserted in the circuit at the connection to 
the hydrophone crystals. The output produced by 
this calibrating voltage is measured and the readings 
are converted to equivalent sound pressure from a 
hydrophone calibration chart supplied by the manu- 
facturer. 



66 


LABORATORY FACILITIES 


2 9 SHOP FACILITIES 

The construction of the apparatus, instruments, 
and experimental test models used by a research 
laboratory requires the services of a variety of shop 
and erection facilities. While all types of work are 
involved, the most important and the most difficult 



Figure 105. Front and rear views of laboratory ampli- 
fying and filtering equipment for 1- to 100-kc range. 

A. Preamplifier E. Voltmeter 

B. 40-db amplifier F. Hewlett Packard oscillator. 

C. Attenuator G. Low-pass filter 

n. 50-db amplifier H. High-pass filter 

I. Hydrophone. 


to obtain in volume is precision machine work. In- 
struments and models particularly require the use of 
specialized equipment and skills not readily available 
in most general shops. Ordinary construction and 



Figure 106. Front and rear views of Naval Ordnance 
Laboratory Mk 3 acoustical unit. 

machine work can be done in most general shops, but 
the special handling associated with single jobs 
causes difficulty in maintaining a continuous flow of 
work. Therefore, some shop equipment directl}^ un- 
der the laboratory supervision becomes a necessity. 

2 ^ ' Model Shop 

The shop facilities of the Hydrodynamics Labora- 
tory were designed to handle the specialized needs of 
a research program. In addition to the normal facili- 
ties for handling the general maintenance and rough 
work, a model and instrument shop is available which 
is equipped to do all types of lathe and mill work, 
pantograph reproductions, and precision drilling, and 




SHOP FACILITIES 


67 


to take advantage of casting and other metal forming 
procedures. A general view of this shop is shown in 
Figure 107. Among its special features are the three- 
dimensional Gorton pantograph machine for con- 
struction of apparatus and models requiring scaled 
duplications of curved and warped surfaces, surface 
grinders and grinding attachments for holding sur- 
face finishes to desired tolerances, and electric and 
induction furnace equipment for specialized casting 
and heat-treating operations. 

To control the accuracy of the work the shop is 
equipped with a toolmaker’s microscope for precise 
measurements and a binocular microscope for use 
while working on small precision parts. Johannson 
gauge blocks are used for miscellaneous precision set- 
ups as well as for standardizing micrometer equipment. 

Special Techniques 

Special adaptations and attachments for the ma- 
chine tools have been developed to meet the particu- 
lar requirements of model construction. As an ex- 


ample, the technique used in forming model bodies 
will be described in more detail. A primary spline jig 
four times model size is produced on the Gorton 
pantograph machine from data giving the two co- 
ordinates of the body shapes and the angle of the 
normals to the curve. In this operation, as shown in 
Figure 108, the milling table is set to the coordinates 
and the drill-guide jig on the tracer table is set to the 
angle of the normal. By this method a double line of 
dowel holes is accurately drilled and reamed in one 
operation along the shape curve. Steel dowel pins 
pressed into these holes securely hold a spring steel 
spline in the proper curve. From this primary spline 
jig a model-size cam plate is produced on the same 
machine, as shown in Figure 109. 

In turning the model part the cam plate is mounted 
on a jig attached to one of the lathes and guides the 
cross feed by means of an air-operated piston, while 
the carriage is moved along by the power feed. Two 
views of this setup are shown in Figure 110. 

The advantage of this technique is that the personal 
element in smoothing in curves from coordinate data 



Figure 107. General view of model shop. 


68 


LABORATORY FACILITIES 


is reduced to a minimum and any number of accurate 
duplicate model shapes may be produced quickly. 

Maintenance and Repair 


Outside Shops 

During the course of the NDRC sponsored proj- 
ects, it has been necessary to rely on the services of 
many outside shops to supplement the volume of 


The general repair and maintenance of the heavier 
and rougher apparatus is handled by a maintenance 



Figure 108. Gorton pantograph machine. 



Figure 109. Production of model-size cam plate. 


shop using different equipment. Lathe and drill press 
equipment, in addition to portable power tools and 
hand tools, are available here. 

General carpentry and cabinet work is carried on 
in a shop operated jointly with the Soil Conservation 
Service Laboratory on the CIT campus. Miscel- 
laneous power tools are available there. 



Figure 110. Two views showing cam plate in use. 

work handled in the Hydrodynamics Laboratory 
shop itself. The additional organizations which con- 
tributed most effectively in the program include the 
Mount Wilson Observatory shop in Pasadena, whose 
facilities were made available on a cost basis through 
the courtesy of the Carnegie Institution of Washing- 
ton; the Fred C. Henson Company, a maker of 
scientific- instruments in Pasadena; and the Astro- 
physics Machine Shop and Optical Shop, both 
located on the CIT campus. 




Chapter 3 

EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 


31 INTRODUCTION 

T he hydrodynamic behavior of submerged mov- 
ing bodies is dependent upon the pattern of 
relative motion of the fluid with respect to the body. 
All the forces arising from such a system of motion 
are caused by the interaction between the body and 
the fluid. The changes in momentum in various di- 
rections caused by the reactions between body and 
fluid are measures of the forces. With each body 
shape there results a particular field of fluid velocities 
and therefore a particular set of forces. Thus there 
are two ways to obtain hydrodynamic forces for the 
analysis of a body’s behavior in motion. First, by 
direct measurement; second, by observing what hap- 
pens to the fluid whose motion the body affects. In 
many respects the latter method, while much the 
more difficult, is the more important. In general, 
direct measurements give overall results. Special 
measurements may indicate but do not explain the 
role played by the various components of a body 
shape. However, a realization of the ways by which 
various shapes affect the flow leads not only to an 
evaluation of the forces but to the ability to predict 
the force changes obtained by shape modification. 

The laboratory has found in the flow line diagrams 
produced in the polarized light flume the means of 
visualizing, qualitatively at least, the relation be- 
tween body geometry and the resulting flow.^ Thus 
even though the picture is too incomplete to permit 
actual evaluation of forces and moments, it repre- 
sents an extremely important design aid. For these 
reasons the assemblage of flow line diagrams for 
various projectiles and projectile components which 
grew up in the course of this project is included in 
this chapter, prefacing several general discussions of 
submerged body behavior. It can be used as a refer- 
ence chapter in which the reader’s picture of fluid 
motion about various shapes can be refreshed from 
time to time. 

The diagrams are constructed from actual experi- 
mental determinations of the flow. The zones of local 
separation and turbulence generation are drawn from 
visual observation of the bentonite suspension. Shear 
patterns are made visible by transmitted polarized 
light, and local flow directions are determined 


through explorations with needle probes and thread 
streamers. The diagrams are intended to represent 
flow directions only. Furthermore, they are, in gen- 
eral, limited to the flow in the plane containing the 
axis of symmetry of the body shape. While this 
representation does not give the entire picture of the 
flow around yawed three-dimensional bodies, it does 
provide an essentially accurate picture of the sense 
and relative magnitudes of the velocity changes in- 
troduced by yawing different shapes. In cases for 
bodies with stabilizing and control surfaces, the flow 
over these surfaces is indicated for planes away from 
the axis. 

The scheme of presentation of diagrams in this 
chapter is based on separation of the projectile into 
its components, the nose, body, afterbody, and tail 
structure, for individual and systematic study. While 
the exact final diagram for any complete body is the 
result of a complex interaction between the effects of 
each component, examples will show how it is still 
possible, with judicious interpretation, to assemble a 
qualitative picture for the whole. For each com- 
ponent several series of diagrams for certain basic 
families are given, followed by diagrams for specific 
designs that were devised by modifying the basic 
profiles. For all bodies the flow is shown around the 
unyawed shape and around the body yawed to 10 
degrees. 

3 2 NOSE SHAPES 

^ ^ ^ Basic Design Shapes 

Selection of the projectile nose shape depends upon 
the requirements of load-carrying capacity (volume), 
length for a given diameter, fluid friction resistance, 
and cavitation limits. The effects of each of these 
requirements are very conveniently studied by sys- 
tematically investigating families of shapes. While 
the families possible are numberless, the ones in- 
cluded here stem from the most familiar and com- 
monly used shapes; ellipsoids, ogives and sphero- 
gives, hemispheres, cones, and various truncated 
shapes including the square-end cylinder. Within 
each of these families will be found a wide range of 
all the variables just listed so that a series of flow 


I vt?^ 


69 


70 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 


line diagrams will yield basic design information 
suitable to aid the selection of basic shapes for given 
projectiles. 

A sensible method for investigating the effects of 
modifications is not so apparent because special pur- 
poses call for special treatment yielding compromise 
shapes. Such modifications are not easily systema- 
tized. Instead, as already mentioned, special flow line 
diagrams are presented for typical groups of modified 
basic shapes. 



Figure 1A. Families of noses. 



Figure IB. Key to noses in Figure lA. 


Figure 1 shows a typical selection of ellipsoids, 
ogives, and spherogives. The basic geometric dif- 
ferences are given in the following paragraphs. Note 
here, however, that an extreme range of geometric 
proportions is illustrated for each family group, with 
variations in the profile and hence the kind of flow 
depending on the group. Thus each family includes a 
continuous series from elongated to blunt shapes. It 
is interesting to note that the hemisphere is a mem- 
ber of each of these three families and that by ex- 
tending the normal geometric definitions, the square- 
end cylinder can also be included. 

Ellipsoids 

Ellipsoids are convenient shapes around which to 
base a nose design for two reasons. First, all propor- 
tions from very blunt to very fine can be conveniently 
described merely by changing the ratio of major to 



3.42: 1 

Figure 2. Ellipsoids. 


minor axes, with fractional ratios for blunt and large 
ratios for fine noses; second, the equations of motion 
for flow around the complete ellipsoid in the ideal 
case are known, so that for the finer noses at least, the 
pressure distribution can be calculated with fair 
accuracy over most of the nose surface. The devia- 
tions from the pressures obtained for real fluids are 
due primarily to the fact that these noses are semi- 
ellipsoids, with a circular cylinder body section re- 
placing the aft half of the true ellipsoid. The ratio of 
major to minor axes as used to describe the noses in 
Figure 2 is for the complete ellipsoid. Thus in prac- 
tice a 23^-to-l ellipsoid makes a nose 134 calibers 
long. 




NOSE SHAPES 


71 


Figure 2 shows the flow line diagrams for a group 
of these ellipsoid noses. In this series note that for all 
shapes flner than the hemisphere, smooth flow with- 
out separation is obtained. With the hemisphere and 
blunter noses separation occurs near or ahead of the 
maximum diameter. 




Ogives 

The ogive as commonly defined is pointed. Blunt 
ogives can be obtained if the geometrical definition is 
modified slightly by assuming that for radii less than 
0.5 caliber (the hemisphere) the nose face is a flat 
disk drawn tangent to the ogive arc. The limiting 
case is then the square-end cylinder where the ogive 
radius is zero. Figure 3 shows the pointed series, 
and Figure 4 the blunt or small-radius series. Pointed 
ogives result in smooth flow patterns without visible 





Figure 3. Ogives. 



(HEMISPHERE) 



0.4 CAUBER 




0 CAUBE:R (SQUARE END CYUNOER) 


Figure 4. Small radius ogives. 


separation even when yawed at 10 degrees. The hem- 
isphere and the small-radius series, however, show 
increasing separation to the maximum obtained with 
the square-end cylinder. 

Beginning with the largest radius ogives, the drag 
should be high because of extra skin friction. As the 
radius is reduced, however, a minimum should be 
reached, beyond which for shorter radii the drag 
should grow again as a result of separation and conse- 
quent increase in form drag. For the square-end 
cylinder, the drag is all form drag and no skin friction. 


72 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 


Spherogives 

The pointed ogive is the shape normally used for 
noses on artillery shells and small arms ammunition. 
For those cases where the velocity is above sonic, the 
sharp point is important in reducing the drag result- 
ing from shock waves. For velocities below the critical 
sonic values, however, ogives often may be shortened, 
while still maintaining the basic advantages of the 
slender nose, by replacing a portion of the point with 
curves forming blunt tips. If the spherical segment is 
used there results the spherogive. For any given ogive 
a series of noses can be formed by drawing in spheri- 
cal segments with larger and larger radii. Each will 
include a greater and greater “half angle” measured 
between the axis and the point of tangency of the 
sphere and the ogive. Such a family is shown in Fig- 
ure 5. If the sphere half angle is maintained constant, 
the nose assumes different proportions as the ogive 



5 CAUBER X 86* 



5 CALIBER X 70* 


Figure 5. Spherogives with constant caliber ogives. 



1.0 CALIBER X 72* 




radius is varied. Figure 6 illustrates this family. In 
both Figures 5 and 6 the hemisphere appears as the 
limiting case. 

Several things are apparent on examination of Fig- 
ures 5 and 6. First, for the 5-caliber series, separation 
of the flow around the yawed projectile occurs for 
sphere half angles larger than 72 degrees. (Note bot- 
tom diagram in Figure 6 as well as Figure 5.) Second, 
for the constant 72-degree half-angle series, separa- 
tion becomes successively worse as the ogive radius is 
decreased. Note also that all the spherogives shown 
permit smooth flow at zero yaw without separation so 
that for bodies which will operate with small yaws 
the spherogive offers a possible way of obtaining 
lower length in calibers or a larger volume for given 
overall length. 

On bodies with sharp curvatures separation occurs 
where the curvature requires too rapid a deceleration 
for the flow to follow the body. Separation from this 






NOSE SHAPES 


73 



40* INCLUDED ANGLE 


jectiles. Simple cones are not regarded as satisfactory 
because of the flow separation at the juncture with 
the cylindrical section, even for very small included 
angles. Figure 7 shows examples of this shape with 
the square-end cylinder as the terminal condition. 
These same shapes with examples of truncated ogives 
are shown in Figure 8. 




100* INCLUDED ANGLE (SQUARE END CYLINDER) 

Figure 7. Conical tapers. 


cause is also an indication of the probable tendency 
to cavitate since low pressures will be obtained in the 
zones of maximum flow curvature usually occurring 
just ahead of the separation zone. Thus the examples 
in Figures 5 and 6 indicate that within limits the 
length of nose can be shortened by using spherical 
tips without affecting the cavitation behavior. 

Conical Tapers 

Tapers in modified forms are used on many pro- 



Figure 8. Conical tapers and truncated ogives. 


Truncated Ogives 

Flat-faced noses formed by truncating ogives have 




I CALIBER OGIVE 




LOG CALIBER x 066 CAUBER FACE 




LOG CAUBER x Q75 CAUSER FACE 






I CALIBER FACE (SQUARE END CYUNOER) 

r'lGURE 9. Truncated ogives. These noses are described 
by the radius of the circular ogival arc and the diameter 
of the flat face, both measured in calibers. 





74 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 


proved important in permitting satisfactory water 
entry for air-launched projectiles. On striking the 



Figure 10. Modified hemispheres. 



surface the flat face with its relatively sharp edge aids 
in creating a cavity of proper diameter to envelop the 
projectile and to avoid interference between the tail 
and water. In addition, as a nose of this type yaws 
the flat face deflects fluid in the direction of yawing, 
giving a reaction in the opposite direction. This ef- 
fect, which occurs whether the nose is completely 
submerged or is wetted only on the disk, gives a 
stabilizing moment that tends to keep the projectile 



Figure 12. Modified ogives and spherogives. 




NOSE WITH 



TOW HOLE 



SPADE NOSE OGIVE 


Figure 11. Modified hemispheres. 


Figure 13. Modified ogives. 




NOSE SHAPES 


75 


CAVITATION ON STABILIZM6 RING NOSE (K=a22) 




77^* CONE X 88^* SPHERICAL SEGMENT 



77f* CONE X 88^* SPHERICAL SEGMENT x 90* CONICAL TIP 





2 CALIBER X 65^* WITH STABIUZING RING 

Figure 14. Modified spherogives. 

on course. This effect of the nose on the flow is shown 
clearly in Figure 9 for completely submerged 
conditions. 

Figure 9 also illustrates the effect of truncating an 
ogive to form successively larger disks. Note that for 
the submerged case if the velocity and pressure con- 
ditions are such that cavitation does not occur, 
relatively large disk areas can be used without exces- 
sive flow separation at the edges and consequent 
relative increase in form drag. 

These noses provide a very low Ijd ratio (relatively 
large volume) when drag and cavitation are unim- 
portant. 

Modified Hemispheres 

The hemisphere in modified form is one of the most 
widely used shapes for all types of projectiles. In 
Figures 10 and 11 are shown several, including the 


extreme example of the “pickle barrel,” a cylindrical 
shell extending the full length of the normal nose. 
Reading down in Figure 11, the third and fourth 
diagrams are noses with fuse projections, the fifth 
shows a version of a Kopf ring. 

The pickle barrel is designed to stabilize an air- 
launched torpedo during its air flight. It has some of 
the characteristics of the truncated ogives and the 
square-end cylinder in that on yawing a stabilizing 
moment results from the pressures arising on the nose 
as the air is deflected laterally in the direction of 





Figure 15. Modified tapers. 


76 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 



Figure 16. Modified tapers. 


Modified Ogives and Spherogives 

Examples of modified ogives and spherogives are 
shown in Figure 12, with flow diagrams in Figures 13 
and 14. Included with these noses are two modifica- 
tions designed to improve water entry, the spade nose 
in Figure 13 and the Kopf stabilizing ring in Figure 
14. The flow line diagrams show that both devices 
introduce extra turbulence and drag. Photographs of 




Figure 17. Modified square-end cylinders. 

yawing. This barrel is destroyed on entry and hence 
does not influence the underwater run. The Kopf 
ring is designed to improve the air-water entry of an 
air-launched projectile. It does so by creating a clean 
cavity of the proper diameter to contain the pro- 
jectile and avoid undue interference and by a tend- 
ency to produce a stabilizing moment for small yaws 
in much the same manner as the square-end cylinder. 
It is clear from the flow line diagrams that on becom- 
ing submerged the extra turbulence created by this 
ring will increase the drag of the projectile. 



Figure 20. Noses with common length. 




NOSE SHAPES 


77 


full cavitation bubbles are shown for both. As is 
discussed in Chapter 4, cavitation cavities so pro- 
duced are similar to the air cavities obtained on 
entry. Note that the cavity actually forms on the 
Kopf ring and tends to envelop the projectile. On the 
other hand, note that each spade forms an individual 
cavity but that the projectile as a whole is not en- 
veloped so that considerable interference and result- 
ant side force can be expected during entry. 

Modified Tapers 

While simple conical tapers are not used normally 
for projectiles, tapers modified mainly by eliminating 
the sharp discontinuity at the base of the cone are 
used. The examples in Figures 15 and 16 are for a 
series of low- velocity rockets. Note that with 
moderate radii at the juncture of cone and cyl- 



2^0 ELLIPSOID 



35 CALIBER I 74* SPHEROOVE 


Figure 21. Noses with the same Ijd back to the 
maximum diameter. 




as CALIBER (HEMISPHERE) 





Figure 22. Ogives. 


inder, smooth flow without separation can be 
obtained. 

Modified Square-End Cylinders 

Eliminating the sharp corner reduced the degree 
of separation and hence the drag. Noses with 
moderate drag coefficients, but still providing for 
good water entry and also having the desirable 
stabilizing moment for small yaw angles when sub- 
merged, can be obtained this way. These noses, 
illustrated in Figure 17, are all for air-launched 
depth charges. 

Modified Truncated Ogive 

Compared with Figure 9 the diagrams in Figure 18 
show little influence of the small irregularities of the 




78 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 


nose profile. The edge of the blunt face provides 
sufficient separation (even though small in magni- 
tude) and hence disturbance in the boundary layer so 
that there are no extra contributions from the down- 
stream projections. 


opposite direction so that cross forces and destabi- 
lizing moments in the direction of yaw can be ex- 
pected. Projectiles with such noses must be stabilized, 
at least during this accelerating period, with fins or 
by spinning. 


Compound-Taper Ogives 

These noses are used for high-velocity projectiles. 
Consequently their flow line diagrams are of interest 






0 CALIBER (SQUARE -END CYUNOER) 

Figure 23. Small-radius ogives. 

only for the short period of acceleration when the 
velocity is below the velocity of sound. The flow dia- 
grams of Figure 19 which are for such noses merely 
show that when yawed the fluid is deflected in the 




5 CALIBER X 86* 




5 CALIBER X 76* 



5 CALIBER X 70* 

Figure 24. Spherogives with constant caliber ogives. 

Noses with Common Length 

A simple example of application of the flow line 
diagram is shown in Figure 21 for the noses pictured 
in Figure 20. The four noses are selected to give the 
same length in calibers, l/d, from the tip back to the 
maximum diameter. The prismatic coefficient, the 
ratio of the nose volume to the volume of a circular 
cylinder of length I and diameter d, is listed for each 
as follows: 

Half body 0.74 

23 ^-to-l ellipsoid 0.67 

1.75-caliber ogive 0.56 

3.5-caliber by 74-degree spherogive 0.79 

The only significant difference in the diagrams occurs 


AFTERBODIES 


79 


for the yawed condition. Note that separation occurs 
for the two bodies having the maximum and mini- 
mum volumes. The ogive radius is so sharp that 
separation occurs on the ogive itself. The spherogive 
tip is so large that it causes separation. This example 
makes it clear tha.t “fineness” alone is not a sufficient 
criterion for selecting a low drag, anticavitating nose. 



1.0 CALIBER X 72* 




Figure 25. Spherogives with constant sphere half angle. 


33 AFTERBODIES 

^ Basic Design Shapes 

Afterbodies, like nose shapes, are in general modi- 
fications of elementary geometric shapes. The follow- 
ing series of families parallel the nose families already 
presented. Each of these diagrams was obtained with 
the afterbody attached to a long cylindrical body 
section so that uniform conditions upstream from the 
afterbody existed. 


Ogives 

In this and succeeding series the effect of blunt- 
ness on the wake formed by separation is empha- 
sized. Note that even for the 5-caliber ogive shown in 
Figure 22 the flow leaves the body surface before the 
tip is reached. The extreme condition, of course, is 
for the square-end cylinder in the small-radius series 
shown in Figure 23. 

Comparison with Figures 3 and 4 emphasizes that 
a shape suitable for application as a nose may not be 
satisfactory as an afterbody. For example, the 1.77- 
caliber ogive when used as a nose causes no serious 
disturbance but, when used as an afterbody causes an 
undesirable eddying wake. Thus it is necessary that 
the afterbody be finer than the nose to produce a 




1.06 CALIBER x Q66 CALIBER FACE 


1.05 CALIBER x a75 CAUBER FACE 


1.05 CALIBER X 033 CAUBER FACE 




I CALIBER FACE (SOUARE-END CYLINDER) 

Figure 26. Truncated ogives. 






80 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 


balanced design with equally satisfactory flow over 
both ends of the projectile. 

Spherogives 

The diagrams in Figures 24 and 25 show some 
similarity to those for the ogives in Figure 22. Note 
particularly that rounding off the 5-caliber ogive tip 
(Figure 22) to form the 5-caliber by 70-degree sphero- 
give (Figure 24) produced very little effect on the 
flow diagram, particularly at zero yaw. 

Truncated Ogives 

The top two diagrams in Figure 26 show that some 
large portion of the ogive tip can be removed with- 
out affecting the flow appreciably. This is similar 
to the effect already observed in forming the spher- 
ogives. 

Comparison of Figure 26 with Figure 22 indicates 
that truncating the 1.05-caliber ogive to a face as 
large as 0.75 caliber produces a disturbance whose 
magnitude is about equal to that for a 0.62-caliber 
ogive. 

Conical Tapers 

Tapers with small included cone angles show 
marked improvement over blunt afterbodies. Figure 
27 serves to emphasize, however, that severe dis- 



80“ INCLUDED ANGLE 



40“ INCLUDED ANGLE 


Figure 27. Conical tapers. 


turbance and consequent undesirable hydrodynamic 
effects are still obtained unless precautions are taken 
to eliminate the sharp discontinuity at the base of the 
cone. 

NO RECESS 



RECESSED 

Figure 28. Spiral flow produced by recesses. 



Figure 29. Afterbodies followed by booms. 
Recessed Afterbodies 

Recesses in blunt afterbodies produce an asym- 
metrical condition that results in a definite spiral to 
the flow in the wake. This effect, which is in contrast 
to the normal wake obtained with the square-end 
cylinder, has been observed for a variety of shapes 
with large recesses at the trailing end, as shown in 
Figure 28. 

^ ^ ^ Specific-Purpose Afterbodies 
Afterbodies Followed by Booms 

Various projectiles, particular!}^ rockets, employ 








AFTERBODIES 


81 



Figure 30. Modified ogive afterbodies followed by 
boom. 



Figure 31. Modified taper afterbodies followed by 
boom. 

booms between the main body and the tail surfaces. 
Figure 29 shows a series of afterbodies designed for 
use with booms. Some of these are modified ogives 
and some are more properly classed as tapers. The 
flow diagrams were all obtained with the booms in 
place. As the diagrams in Figures 30 and 31 show, the 


flow separation in each case occurs along the surface 
of the afterbody proper so that irregularities at the 
boom connection contribute little additional dis- 
turbance. 



Figure 32. Fine afterbodies. 




Figure 33. Fine afterbodies. 



82 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 



Figure 34. Modified conical afterbodies. 


Fine Afterbodies 

Several torpedo afterbodies whose shapes are ap- 
proximately ogival, or ogival with conical tips, are 
shown in Figure 32, with their flow diagrams in Fig- 
ure 33. The importance of using the longer, finer 
shapes for afterbodies is emphasized here. A relatively 
fine body is necessary before flow is obtained with- 
out appreciable disturbance ahead of the trailing 
tip. 

Figure 34 shows two depth bomb afterbodies of 
modified cones. The relative magnitudes of the dis- 
turbances and the resulting wakes are indicative of 
the degree to which discontinuities in the surface 
profile have been suppressed. 

The influence of tail structures such as shown in 
these figures will be discussed in a later section in this 
chapter. 

Rocket Nozzles 

Rocket nozzles are located either at the end of a 
boom, and hence are of a smaller diameter than the 
main body, or are incorporated as part of the after- 
body proper. Nozzles on booms are shown in Figures 
35 and 36. Nozzles in afterbodies are shown in Figure 
37. 

Elimination of disturbances by streamlining can be 
readily accomplished in various degrees up to the 
point where the nozzle area equals the boom diameter 
(compare last diagram in Figure 35 with Figure 36). 
It should be noted, however, that such streamlining 
of the flow is not a desirable feature for all cases. As 
will be discussed in more detail with respect to tail 
structures, the drag from the disturbances such as 


shown in Figure 35 produces a stabilizing moment 
when the projectile is yawed. Consequently for cer- 
tain low- velocity projectiles where drag is relatively 
unimportant, this effect may be a desirable contri- 
bution. 

The diagrams in Figure 37 illustrate examples with 
various degrees of streamlining. The effects of the 
tail surfaces (fins and ring) such as shown in Figures 
35, 36, and 37 will be discussed later. 



Figure 35. Rocket nozzles. 


Effect of Components of a Nozzle Assembly 

Figure 38 illustrates a typical example of varying 
one of the components of a tail nozzle assembly. 

Figure 39 shows the effects of step-by-step addi- 
tions to a complete assembly. As stated in the intro- 




TAILS 


83 


duction, the flow diagram for the complete projectile 
is not necessarily the summation of the diagrams for 
the individual components. In this example each 
component introduces a radical change in the dia- 
gram. 



Figure 36. Rocket nozzles. 


TAILS 

^ Purpose of Tails 

Generally speaking it is the purpose of tail surfaces 
to provide an otherwise unstable projectile with a 
desired degree of Static and dynamic stability. In the 
case of certain missiles, such as torpedoes, adjustable 
tail surfaces permit control of the projectile trajectory 
as well. 

^ ^ ^ How Tails Work 

Tail surfaces are effective in producing static 
stability because, when a projectile yaws, the tail 
deflects some fluid and as a result is subjected to a 
force proportional to and in the opposite direction to 
that at the change in the fluid momentum. This force 
will have a lateral or cross force component and a 
drag component. The resultant of this force and the 
skin friction drag on the tail will cause a moment 
about the projectile’s center of gravity. The fact that 
both drag and cross force components can be made to 
produce stabilizing moments leads to two methods of 
creating a required moment. It can be obtained either 
by a high-drag (and usually low-lift) shape or by a 





Figure 37. Rocket nozzles. 

high-lift (and usually low-drag) shape. Vector dia- 
grams illustrating these two combinations are shown 
in Figure 40. It is clearly seen that for the same 
resultant force the moment is much larger if a high 
cross force rather than a high drag is obtained. Nev- 
ertheless, some designs do make use of high drag as a 
means of getting additional stabilizing moment. The 
normal designs of fin tails, ring tails, and square box 
tails are structures intended primarily to produce 
large cross forces with yaw. 

In addition to producing moments as described, 
when a projectile yaws, stabilizing surfaces also 
provide additional damping forces, and hence damp- 
ing moments, to contribute to the dynamic as well as 
static stability. This effect cannot be studied by the 
flow line diagrams which are for the static, or steady- 





84 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 



Fi CURE 38. Effect of tail disks on terminal disturbance. 


state, conditions only. A more thorough discussion of 
stabilizing surfaces and static and dynamic stability, 
together with quantitative test data, is given in 
Chapters 9 and 1 1 . 

* Plain Fin Tails 

Fixed and Collapsible Fins for Rockets 

Figures 41 and 42illustratefour very different types 
of fin tails for rockets. Fins on the first three are 
fixed, fins on the last (bottom diagram) are designed 
to fold forward for insertion into a launching tube 
of the diameter of the main body of the projectile. 
On launching, the fins fly open as shown for air 
travel. 

At zero yaw, tail fins are ineffective. When yawed, 
the diagrams illustrate how the fluid is given a change 
in direction producing a lateral force on the fin sur- 
face. Within certain limits a given force can be ob- 
tained by a long fin with a short span, or by a very 
narrow fin with a wide span. The collapsible fins are 
of the latter type. Figures 43 and 44 show three de- 
signs of collapsible fins for the bazooka rocket 


suggested to replace the original tail shown second 
from the top in Figure 44. Both radial and raked fins 
are illustrated. Actually the radial fins in these fig- 
ures produce much more cross force than the original 
tail. The only essential difference in the flow picture 
is caused by the flanged fin tips in the top two 
diagrams. With the radial fins the flange is in- 







Figure 40. Diagram showing the effect of change of 
moment arm P as cross force and drag change even 
though resultant force on tail remains unchanged. 



TAILS 


85 


dined to the flow resulting in some disturbance at 
zero yaw. The raked fins are tilted back until the 
flange is in line with the flow and hence causes no 
disturbance. 

The long narrow vanes used on collapsible fin tails 
are subjected to -severe bending forces during the 
initial launching period before the fins unfold. Figure 
45 shows the flow over a typical folded tail, a typical 
diagram of the forces produced with yaw, and a 
photograph of a fin which was bent from the folded 
position during tests in the water tunnel. As the 
vector diagram indicates, a large normal force is 
easily obtainable on the fin at some distance forward 
of the hinge. The resulting bending moment can 
easily damage an unreinforced fin. Note that two of 
the tails in Figures 43 are constructed with fins rein- 
forced with longitudinal flutes. 


Fin Tails with Adjustable Rudders 

Torpedoes require adjustable tail surfaces to create 
the variations in cross forces and moments necessary 
for the control of the projectile motion. Figure 46 
shows three different designs with fixed fins followed 



Figure 41. Plain fin tails. 


by movable rudders. Zero- and 10-degree yaw dia- 
grams for rudders neutral and rudders down are 
shown. The added effect of the very small rudder area 
is small for these cases. In addition to showing how 
the fins and rudders act to produce a lateral force, the 
diagrams emphasize the desirability of maintaining 
close clearance between the rudder and fin. In the 
bottom diagram considerable flow through the wide 
gap and hence loss in cross force results on yawing. 

Ring Tails and Square Tails 

Rings with Ogival Afterbodies 

The cross force developed on a ring tail as a pro- 
jectile is yawed occurs when the ring surface is at an 








86 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 



Figure 43 . Collapsible fin tails. 


“angle of attack’ ' with respect to the flow past it. At 
zero yaw, on the other hand, additional undesirable 
drag is obtained unless the ring surface matches the 
flow lines around the ringless afterbody. Thus, de- 
pending on the shape of the afterbody, the ring may 
be cut from either a right cylinder or a cone. For the 
various ogival and tapered afterbodies, the cone 
angle can be adjusted to meet the flow conditions. 
The cone angle is defined as the included angle be- 
tween the inner chords of the ring on an axial cross 
section; thus it is twice the angle of the flow measured 
from the projectile axis. 







Figure 44 . Collapsible fin tails — radial and raked fins. 

V(X)NFii)i:vnAt^ 



TAILS 


87 


An example of the matching of ring tails to flow 
lines is shown in Figure 47. The flow past the ringless 
afterbody shows an angle of 4 degrees at the fin tip 
where the ring is to be placed, calling for an 8-degree 
conical ring. The best fit to the flow lines was actually 
obtained with thi-s cone angle as may be seen by com- 
paring the flow lines for the cylindrical ring and the 
8-degree and 16-degree rings shown in Figure 47. 
Photographs of the same three rings are shown in 
Figure 48. Additional examples are shown in Figure 
49 of rings fitted to afterbodies finer and also blunter 
than those in Figure 47. The cylindrical ring on the 
blunt afterbody causes a disturbance of the flow lines 
which is avoided with the correctly matching 12-de- 
gree ring. Note that all the rings shown were con- 
structed with true cylindrical or conical inside sur- 
faces. The outside surface was machined to make the 



Figure 45. Large bending forces exist on folded fins. 


cross section of the ring, taken through the cone axis, 
a streamlined shape. 



Figure 46. Fin tails with adjustable rudders — each 
pair shows rudders neutral and rudders down. 



88 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 





CYLINDRICAL RING 





8* CONICAL RING 



16* CONICAL RING 


Figure 47. Matching ring tails to flow lines. 



12* CONICAL RING 
"BLUNT" AFTERBODY 



Figure 49. Matching ring tails to flow lines. Ring sec- 
tion is streamlined with conical inside surface and curved 
outside surface as shown. 



Figure 50. Ring tails. 



Figure 48. Matching ring tails to flow lines. 


Figure 51. Ring tails. 


^iJ^HI)K\T'TAj3 





TAILS 


89 


Rings on Rocket Booms 

The effectiveness of a ring (as well as the simple 
fin) depends on it being located so as to extend be- 
yond the zone of fluid decelerated by the body into 
the high-velocity fluid. The location as well as the 
design of the ring therefore will depend on the body 
shape. Typical rings for rockets with cylindrical 
booms, tapered afterbodies, and irregular nozzles on 
booms are shown in Figures 50 and 51, and with flow 
diagrams in Figures 52, 53, 54, and 55. 

In Figure 52 the effect of ring diameter (width). 



2 CALIBER WIDE x 2 CALIBER LONG 



2 CAUBER X I CALIBER 




2 CAUBER X f CALIBER 


ii CAUBER X f CALIBER 



2 CALIBER X I CALIBER IN FORWARD POSITION 

Figure 52. Ring tails on cylindrical rocket boom. 





Figure 53. Three applications of ring tails to rocket- 
propelled bodies. 



Figure 54. Ringtails on rocket booms. 


length, and ring location are illustrated for cylindrical 
booms. The top two diagrams show about the same 
effect on the flow pattern. This is a qualitative indi- 
cation that for a given diameter the effectiveness of 


/'(:(AHI)fc.VI.Ln~ 7 



90 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 




I 

' 

1 



Figure 55. Effect of supporting fin area and snugness 
to body. 



Figure 56. Ring tails on extended interior fins. 


the tail is not improved if a certain optimum length is 
exceeded. This fact is borne out by actual measure- 
ments (see discussions in Chapters 9 and 14). The re- 
sistance to flow through the narrow passage left in- 
side the small diameter ring shown in the fourth 
diagram causes some of the fluid to by-pass the ring 
and hence reduces the cross force. The small arrow at 
the top of the yawed ring marks a disturbance result- 
ing from the flow “spilling out.’’ The tail with the 


ring moved forward as shown in the bottom diagram 
is less effective than for the same ring at the end of 
the boom, also because there is greater resistance to 
flow through the annular space inside the ring. In 
Figure 54, the effects of different attachments to 
rocket nozzles are shown. These show the advantage 
of providing large passage and good access to en- 
courage as much fluid as possible to pass through the 
ring. The effectiveness of the increased supporting fin 
area in deflecting the fluid is shown by comparing the 
top three diagrams with the lower three in Figure 55. 

Ring Mounted on Extended Fins 

Ring effectiveness can be increased if the ring can 
be supported aft of the projectile proper. Not only 



Figure 57. Ring tails on extended interior fins. 


4:()NHPF-)lTtg3 




TAILS 


91 


is the distance to the center of gravity of the pro- 
jectile increased, but on yawing the ring extends out- 
side the wake of the projectile body into high-velocity 
fluid. Figures 56 and 57 are examples where the fins, 



Figure 58. Ring tails on extended exterior fins. 



Figure 59. Ring tails designed for high drag. 



Figure 60. Ring tails designed for high drag. 


which are primarily supporting struts, and the 
rings are restricted to the diameter of the projectile 
body. Note that in the first three cases the fins 
must be arranged to provide for expanding exhaust 
gases. 

Where an extra large cross force and restoring 
moment is required, large fins can be used which ex- 
tend from the ring radially or longitudinally. Ex- 
amples are shown in Figure 58. Some of these tails are 
poorly designed for their purpose. The second design 
with the two separated rings is less effective than if a 
single ring of twice the length were used at the end of 
the boom. This construction, however, does add to 
the mechanical strength. Similarly if there are no 
clearance limitations a much more effective design 





92 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 




SAME AFTERBODY AT 90* ORIENTATION 



Figure 61. Square (box) tails following conical after- 
bodies. 


can be obtained than shown in the lower diagrams, 
by increasing the ring diameter as well as the fin 
span. 

Ring Tails for High Drag 

As already discussed, a high-drag tail is not an 
efficient means of providing a stabilizing moment. 


However, it probably represents the best method of 
maintaining a low terminal velocity. High drag due 
to any other component of the projectile reduces the 
stabilizing moment under yaw. This is particularly 
important if the sonic velocity range is approached. 
The formation of shock waves on the nose should 
result in increased sensitivity to yaw. 

Figure 59 shows two designs, one of which can be 
oriented in either direction, as shown in flow line 
diagrams of Figure 60. The drag of the cone with the 
small-diameter end forward greatly exceeds the drag 
of the other two examples. 



Figure 62. Square tails. 


Square Tails 

The principles for design of square tails parallel 
those for ring tails. Examples of these box tails on the 
conical afterbodies of several Service bombs are given 
in Figure 61. Models of two of the versions are 
illustrated in Figure 62. 


^ ^ ® Special Application 

Ring Tail with Exhaust Stack 

Torpedo exhausts carried through the propeller 
hub complicate the mechanical design. Figure 63 
shows the diagram for a design using the ring tail and 
its supporting fin as an exhaust duct. For this arrange- 
ment the diagram makes it clear that a tail pipe is 
necessary to extend the exhaust aft of the propeller 
disk so as to avoid interference with the propeller and 
consequent loss of thrust. 





THE USE OF FLOW DIAGRAMS IN DESIGN 


93 



3 5 the use of flow diagrams 

IN DESIGN 

^ Effects of Subassemblies 

on Assembled Units 

As discussed in the introduction to this chapter, 
the flow diagram for a complete projectile represents 
all the interdependent effects of the components. To 
be sure, certain details can often be examined sepa- 
rately, resulting in conclusions independent of the 
shape of the whole. Care must be taken, however, to 
assure that this is true. For example, Figure 64 shows 


local flow disturbances around rivets and suspension 
fittings as examined separately. Figure 65 shows the 
flow diagram for similar suspension fittings on a com- 
plete torpedo. There is no essential difference in the 
conclusions reached about the effects of these fittings 
on the flow and drag. Figure 66, on the other hand, 
shows such fittings on a depth bomb. A discontinuity 
at the junction between the nose and the full di- 
ameter body results in flow separation and a wake 
which completely envelops the suspension fittings. 
As a result, extra drag should not be expected from 
these protrusions in the latter case. This conclusion 
was verified by water-tunnel measurements. 

The cases where complete diagrams can be assem- 
bled from those of the components are numerous, 
however. An example is shown in Figure 67. 



Figure 64. Local disturbances by rivets and sus- 
pension fittings. 




Figure 65. Suspension fittings on streamlined projectile. 


94 


EFFECT OF PROJECTILE COMPONENTS ON THE FLOW DIAGRAM 



Figure 66. Suspension 6ttings in wake of blunt nose. 



THE USE OF FLOW DIAGRAMS IN DESIGN 


95 





TAIL 



Figure 67. An example of the use of flow diagrams in combining projectile flow components. 



Chapter 4 

CAVITATION AND ENTRANCE BUBBLES 


INTRODUCTION 

AN AIR-WATER PROJECTILE, such as an aircraft tor- 
pedo, in the course of its trajectory from the air- 
plane to the underwater target, passes through at 
least one, and possibly two, transient conditions in 
which its entire performance may be affected signifi- 
cantly by phenomena involving both a gas and a 
liquid. The first of these begins at the instant of water 
impact, and continues as long as the air that has been 
carried down into the water by the projectile stays 
with it as a bubble that covers at least a portion of 
the projectile surface. The second condition occurs if, 
during the subsequent underwater run, the reduction 
of pressure resulting from the velocity of the body be- 
comes, at some points on the projectile, equal to the 
vapor pressure of the water at the existing tempera- 
ture. If this happens, evaporation will occur at these 
points, forming small vapor-filled bubbles. These 
small bubbles, under certain conditions, may be 
formed in increasingly higher numbers covering an 
increasingly larger surface. If conditions become 
more favorable to their formation, they combine to 
produce a large cavity or bubble which normally 
appears as a band encircling the projectile. If condi- 
tions become still more favorable, the cavity may 
grow until it envelops the entire downstream portion 
of the body. This phenomenon is called cavitation 
and its different stages are known as incipient, partly 
developed, and fully developed cavitation. Any of 
these stages may be the equilibrium stage and thus 
prevail for any length of time, and, therefore, be 
subject to study. Unlike this, the different stages of 
the air bubble formed at the water entrance of the 
projectile are continually changing, thus making the 
phenomenon transient in the strictest sense. The di- 
rect investigation of this transient phenomenon is far 
more difficult. Furthermore, cavitation can be stud- 
ied on a stationary body surrounded by a moving 
fluid, but, even in the laboratory, entrance bubbles 
must be studied on moving bodies. 

On the other hand, the similarity of the air enve- 
lope formed after the entrance of the projectile into 
water, and the vapor envelope of fully developed 
cavitation suggests that they are, in many respects, 
manifestations of the same basic phenomenon, even 


though in the past they were considered as wholly 
unrelated. 

In view of the similar characteristics of the two 
manifestations and the relative difficulty of making 
quantitative studies on moving bodies, the main 
basic investigations were carried out in the cavita- 
tion field. However, to form a basis for discussing the 
application of the cavitation results to the water- 
entry problem, the main features of the entrance 
bubbles will be reviewed first, so that during the pre- 
sentation of the results of the cavitation study, it 
will be possible to point out the similarities and 
differences of the entrance and cavitation bubbles. 

*2 ENTRANCE BUBBLES 

As a projectile, having a moderate or high speed, 
first touches the surface of the water, the latter is 
forced away from the point of contact. This action is 
so violent that it gives rise to the common description 
that the projectile “blows a hole for itself in the wa- 
ter.” This cavity may be considerably larger in di- 
ameter than the projectile, and many times its 
length. During its formation it is open to the atmos- 
phere and, therefore, is filled with air at or slightly 
below atmospheric pressure. As the projectile pene- 
trates farther into the water, the cavity continues to 
lengthen until a point is finally reached when the 
water closes in, severing the connection between the 
cavity and the atmosphere, and changing the cavity 
from an open tube into a closed bubble. This bubble 
continues to travel forward with the projectile. How- 
ever, from the instant of closure, the amount of air 
within the bubble diminishes because it is entrained 
by the water through which it is moving until it 
finally disappears completely. Figure D shows such a 
cycle. This cavity, from the instant of its inception as 
the tip of the projectile first touches the water until 
its final disappearance as the last particle of air is 
swept away from the surface of the projectile, is com- 
monly referred to as the entrance bubble. 

As the projectile touches the water the drag goes 
up tremendously, primarily because of the great in- 
crease in density of the water over the air, and 

“ These pictures were taken in the model tank at the Naval 
Ordnance Laboratory, Washington. 


96 


CAVITATION 


97 




C 

K = 0.54 


Figure 2. Cavitation bubbles. 


*3 CAVITATION 

* ^ ^ Definition of Cavitation 

In this discussion cavitation will be taken to mean 
the generation of a gas space, or bubble, in a liquid, 
this space being filled primarily with the gas phase of 
the liquid, at the same temperature as the liquid, and 
at the equilibrium pressure for that temperature. So 
far all of these requirements could be filled by gas 


stages of the bubble formation, the nose is the only 
point of contact. Hence the point of application is 
ahead of the center of gravity, and for any normal 
nose shape the condition is unstable. The lateral 
component of this force acts to produce a rotation 
about a transverse axis through the center of gravity, 
and this rotation continues until a restraining force is 
developed when the afterbody or tail structure comes 
in contact with the wall of the bubble. Since all of 
these forces are large, they greatly affect both the 
velocity and the direction of the motion of the 
projectile. 

We note the entrance cavity is an air bubble, and 
although there may be traces of water vapor or other 
gases present, they play no significant part in the 


POINT I 


POINT 2 


Figure 3, Flow diagram. Mk 13 Torpedo nose, 

bubbles formed in a boiling liquid. This is not sur- 
prising, since the cavitation voids are filled with gas 
by evaporating a portion of the surrounding fluid, 
i.e., by boiling. However, in most processes where a 


secondarily because, as far as the water is concerned, 
the shape of the projectile is that of the entrance 
bubble, and this in general is less streamlined than 
the projectile, and thus has a higher form drag, as well 
as a larger cross section. Furthermore, the entire 
force distribution -on the body is radically altered. 
During the air flight, the aerodynamic forces are the 
result of the skin friction and the pressure distribu- 
tion over the entire body, whereas in the entrance 
bubble the only existing forces of significant magni- 
tude are applied in the very small areas of contact 
between the projectile and the water. In the initial 


Figure 1. Entrance bubble cycle from model tank. 


phenomenon. Its superficial similarity with cavitation 
may be recognized by comparing the cavitation 
pictures, shown in Figure 2, \vith the entrance 
bubbles of Figure 1. 


A 

K = 0.19 


B 

K=0.2I 




98 


CAVITATION AND ENTRANCE BUBBLES 


liquid comes to a boil the liquid is either stationary 
with respect to the container or moving at a velocity 
so low that it has no appreciable effect on the pres- 
sure. Thus, the pressure is sensibly the same through- 
out the liquid, varing only with the depth. In cavita- 
tion, however, the velocities in the cavitating zone 
must be high, because they are the cause of the drop 
in pressure from the static pressure, which is well 
above vapor pressure, down in vapor pressure itself 
at the point where the cavity is formed. This drop in 
pressure which accompanies an increase in velocity 
is in accordance with the principle of the conserva- 
tion of energy, as expressed in the Bernoulli equation. 
Consider a stream tube in the flow pattern in Figure 



Figure 4. Cavitation damage to runner of centrifugal 
pump. 


3. If the Bernoulli equation is written between points 
1 and 2, which lie in a horizontal plane, it becomes 

V)} V2^ 

Pi + P Y = P2 + Py 
or 

P2 = Pi + y + V2^) 

where p is the density of the fluid, and pi and p 2 are 
the pressures, and Vi and V 2 the velocities, at points 1 
and 2, respectively. Another striking difference be- 
tween the cavitation phenomenon and usual boiling 
is seen when the possibility of collapse of a vapor 
bubble is examined. In the boiling liquid a gas bub- 
ble, once formed, tends to rise due to its buoyancy, 
and as it rises, the pressure on it decreases due to the 
decreasing hydrostatic head. Thus, even though no 
more vapor passes into the bubble, it will expand un- 
til it reaches the surface. Now, a vapor bubble formed 
by cavitation will also tend to rise due to buoyancy. 
However, in most cases, the upward velocity due to 


the buoyancy is negligibly small compared to the 
velocity of flow of the surrounding liquid. Therefore, 
the path of the bubble is determined by the flow of 
the liquid. If the liquid carries the bubble to a region 
where the pressure is higher, the bubble will collapse 
because the vapor is no longer in equilibrium with the 
liquid, i.e., it condenses. Since in this condensation 
the vapor disappears entirely into the liquid phase, 
there is no gas to cushion the collapse. Therefore, 
when the liquid surfaces meet or when a liquid sur- 
face collapses against a solid surface forming a part 
of the bubble boundary, the “water hammer pres- 
sure” which results can be extremely high. These 
high forces are probably responsible for the pitting 
of metal surfaces that is commonly associated with 
continued cavitation. An extreme case of cavitation 
damage on the runner of a centrifugal pump is shown 
in Figure 4. However, the principal objective of this 
discussion is to investigate the phenomenon of cavi- 
tation itself and not the damage resulting from it. 
Therefore, cavitation damage will be given no further 
consideration. 

^ ^ ^ Location of Point of 

Cavitation Inception 

From the preceding description of the nature of 
cavitation, it is obvious that if the pressure distribu- 
tion is known, then the point of cavitation inception 
can be determined immediately. Cavitation obviously 
will occur first at the point of minimum pressure on 
the body. It will commence when this pressure reaches 
the vapor pressure of the fluid. If the surface of the 
submerged body be thought of as a deflecting or guid- 
ing surface for the flowing fluid, a rough estimate can 
be made of the critical points on the body where low 
pressures might be expected. Thus, parts of the sur- 
face which deflect the flow away from the body will 
be regions of high pressure and, therefore, will not be 
susceptible to cavitation. Conversely, those parts of 
the surface which fall away from the flow and thus 
deflect it so that the flow lines are concave toward 
the body are low-pressure regions, and hence zones in 
which cavitation may be expected to appear. Con- 
sider a typical projectile, such as the torpedo shape 
which is shown, together with its pressure distribu- 
tion, in Figure 5. The tip of the nose is always the 
high-pressure region because it is deflecting the flow 
away from the body. However, considerably before 
the cylindrical portion is reached, the nose surface is 
falling away from the lines of flow, and hence, a low- 


CAVITATION 


99 


pressure region can be anticipated. If cavitation 
occurs in this region, as shown iri Figure 6, it is usu- 
ally referred to as nose cavitation. The amount of 
lowering of the pressure below that of the neighbor- 
ing undisturbed liquid is, for a given velocity, de- 




.57 9 to 


n ii 13 14 I 's 16 i7 

LOCATION OF PRESSURE TAPS 




Figure 5. Mk 25 torpedo shape. Pressure distribution 
along longitudinal section. Yaw angle 0 degree. 


body come together and are forced to lose their radial 
component of velocity. 

If the body has fixed or movable fins, the leading 
edges will be high-pressure regions. However, by 



Figure 7. Afterbody cavitation. 

analogy to the flow around the nose, these edges will 
be followed immediately by low-pressure regions, and 
hence, as in Figure 8, will be another possible source 
of cavitation. If the projectile is a torpedo, the pro- 
pellers will offer another possible location for cavita- 
tion, as seen in Figure 9; a very likely one in fact, be- 
cause they are nothing more than moving fins, and 



Figure 8. Fin cavitation. 


termined by the shape of the nose. It is to be expected 
that the cylindrical part of the body will be a zone of 
rather uniform pressure since it has no means for 
causing any radical change in the flow direction. 
However, as soon as the body starts to decrease in 
diameter towards the tail, another low-pressure re- 



Figure 6. Nose cavitation. 


gion will be formed. If this has a lower pressure than 
the corresponding region on the nose, cavitation will 
first occur here, as in Figure 7. Finally, a high- 
pressure zone can be expected toward the aft end 
where the flow lines that follow the tapering after- 


their rotation means that they have a higher velocity 
with respect to the water than do the fins. This higher 
velocity may result in correspondingly lower pres- 
sures, and hence, additional cavitation regions. It is 
possible to conceive of a body so designed that each 
of these four zones would have the same pressure and 



Figure 9. Propeller cavitation. 


hence, when the pressure held was lowered they 
would all reach vapor pressure at the same instant, 
. and four independent zones of cavitation would be 
formed. Figure 10 shows a body upon which cavita- 






100 


CAVITATION AND ENTRANCE BUBBLES 


tion starts in several different zones at nearly the 
same time. In practice, however, this is rarely the 
case. One zone usually has a lower pressure than the 
other and cavitation becomes evident there first. 
If the pressure field continues to drop, the zone of 
next lowest pressure will start to cavitate, and so on. 
Often, however, the growth of the cavitation bubble 
at the first zone is so rapid that it envelops the other 
zones before they would have reached cavitation 
conditions if the flow had remained undisturbed. 
This growth of the bubble will be discussed in more 
detail later. 



Figure 10. Body with several points of simultaneous 
cavitation. 


It may have been inferred from the previous re- 
marks that visible cavitation always occurs at the 
point of minimum pressure on the body. This is not 
strictly true. When the minimum pressure point co- 
incides with a geometric discontinuity, the visible 
cavitation usually appears at the same location. 
However, if the discontinuity is sharp enough, the 
cavitation may even appear first in the fluid at some 
distance from the body. For shapes with reasonably 
large radii of curvature, the visible cavitation usually 
appears somewhat aft of the point of minimum 
pressure. 

* * ^ Cavitation Parameter 

In order to describe quantitatively the conditions 
under which cavitation occurs, the cavitation para- 
meter K has been defined as follows: 


^2 ^ V-/ 

'’T 

in which Pl = absolute pressure in the undisturbed 
liquid, 

Pb = absolute pressure in the bubble or 
cavity, 

V = velocity of the projectile with respect 
to the undisturbed liquid, , 

0 = density of liquid. 


Note that any homogeneous set of units can be used 
in the computation of this parameter. It is often 
convenient to express this parameter in terms of the 
head, i.e., 

^ (la) 

where Hl = the submergence plus the barometric 
head, in feet of liquid ; 

Hb = absolute pressure in the bubble, in feet 
of liquid; 

g = acceleration of gravity, in feet per sec- 
cond per second; 

v'^/2g = the velocity head, in feet of liquid. 

Any unit of length can be used in equation (la) in- 
stead of feet. It will be seen that the numerator of 
both expressions is simply the net pressure or head 
acting to collapse the cavity or bubble. The denomi- 
nator is the velocity pressure or head. Since the pres- 
sure reduction at any point on the body is propor- 
tional to the velocity pressure this may be considered 
as a measure of the pressure available to open up a 
cavity. From this point of view, the cavitation pa- 
rameter measures the ratio of the pressure available 
to collapse the bubble to the pressure available to 
open it. If the K for incipient cavitation is considered, 
it can be interpreted to mean the maximum reduction 
in pressure on the surface of the body, measured in 
terms of the velocity pressure. From this it follows 
that, if a body starts to cavitate at K = l, the lowest 
pressure at any point on the body is I velocity pres- 
sure below that of the undisturbed fluid. Figure 5 
presents a concrete example of this relationship. It 
shows the measured pressure distribution on the sur- 
face of a torpedo, expressed in terms of the velocity 
pressure. The lowest pressure occurs at the junction 
between the spherical nose and the conical section. 
The pressure at this point is 0.72 of a velocity head 
below that in the undisturbed fluid. Under cavitation 
tests in the water tunnel, this same shape cavitates 
first at this location, and the measured K for incipient 
cavitation is 0.67. 

It will be seen that the K for incipient cavitation is 
a measure of the resistance of the body to cavitation, 
or in other words, an indication of the excellence of 
the shape. Thus, the lower the K for incipient cavita- 
tion, the greater the cavitation resistance, and the 
better the shape from this viewpoint. 

It should be borne in mind that the cavitation 
characteristics of a given body are not defined by a 


/ coNriDi.x ri v i. 



CAVITATION 


101 


single value of K. For example, a specific torpedo 
shape might show signs of incipient cavitation on the 
nose at a particular value of Ki. With a slightly 
lower value K 2 , cavitation might commence on the 
fixed fins. Careful examination of the propellers 
might demonstrate* that cavitation had commenced 
on them at a value Kz, which was even greater than 
Ki. A value might be recorded at the start of 
cavitation on the afterbody. At A5, the length of the 
cavitation bubble on the nose might be observed to 
be equal to 2 body diameters. 

The preceding paragraphs illustrate the fact that 
the cavitation parameter K, has many uses. Two of 
these should be noted explicitly. The first one is that 
for a given projectile, each specific bubble configura- 
tion from the point of inception to the development of a 
bubble of “infinite” length corresponds to a specific 
value of K. It thus serves to define, for one given 
shape, the degree of cavitation. The second use is 
that in comparing different projectiles or different 
parts of the same projectile, it serves as a yardstick 
for the evaluation of their relative performances. 
This use has been demonstrated in the two preceding 
paragraphs. 

It may have been noted that in defining the cavita- 
tion parameter there has been no discussion concern- 
ing what determines the pressure within the bubble. 
This was done deliberately because the pressure in 
the bubble may be determined by a number of dif- 
ferent factors which have no effect on the interpreta- 
tion of the parameter. Thus, it is quite immaterial 
whether the bubble contains air under pressure, 
products of combustion, or water vapor in equilibrium 
with the surrounding water. However, if the cavita- 
tion void is filled only with water vapor in equilib- 
rium, then the phenomenon is that of “true cavita- 
tion” as normally defined. In this case, Pb becomes 
the pressure of the vapor, which can be determined 
from tables of the vapor pressure of sea water or fresh 
water, as the case may be. Figure 11 has been con- 
structed to assist in the determination of A for such 
cases. This diagram clearly shows the effect of depth, 
or submergence, and velocity. (Also see Appendix.) 

It should be noted that although, under service 
conditions, the pressure on the water surface can 
vary only by the normal barometric fluctuations, 
very different conditions can be established in the 
laboratory, where, for example, the “atmospheric” 
pressure is completely under control. Thus, in the 
high-speed water tunnel, shapes can be made to cavi- 
tate at much lower velocities than would be possible 


in the free ocean, simply by reducing the system pres- 
sure until the K is reached at which the desired de- 
gree of cavitation is obtained. For example, take the 
case of a projectile which runs in the ocean at 5-ft 
submergence and has a A for incipient cavitation of 
0.45. The velocity at which cavitation commences is 
given by equation -{la). 

2g{hL - hs) |/64.4(33.2 + 5 - 0.4) 

A y 0.45 
= 73.8 fps" 

If a model of this projectile is tested in the water 
tunnel, and if the tunnel pressure, l is reduced, say, 
to 15 ft abs, the velocity for incipient cavitation re- 
duces to 

l/64.4(15 - 0.4) ^ 

'' = V 0l5 = 

A further reduction of /iL to 5 ft abs, would cause the 
cavitation to start at 25.6 fps. If with h l equal to 5 
ft abs the velocity were maintained at 45.7 fps, A 
would be reduced to 0.14 and extremely heavy cavi- 
tation would be caused, resulting in a bubble several 
times as long as the projectile. 

^ ^ ^ Degrees of Cavitation 

One of the most significant cavitation character- 
istics of a body is its A for incipient cavitation. How- 
ever, this by no means describes its entire cavitation 
performance even if consideration is given only to the 
single zone in which cavitation first commences. For 
example. Figures 12A to G represent the develop- 
ment of cavitation on a typical body with a hemi- 
spherical nose. It will be observed that as the cavita- 
tion parameter decreases, the cavitation zone 
lengthens. It has been found in the laboratory that 
for a given shape of body and constant yaw angle, 
the relationship between the length of the zone and 
the value of A is a fixed function of that shape, thus, 
as suggested earlier in this section, A can be used to 
describe the degree of cavitation as well as the begin- 
ning of it. 

Since, for a given value of A, the cavitation bubble 
has a fixed size and location with respect to the body, 
from the point of view of the liquid, the shape of the 
body has been altered by it. Thus, as far as the liquid 
is concerned, it is flowing around an object which has 
the overall shape of the original body plus the cavi- 

b 33.2 ft of sea water at 50 F = 1 atm. At this temperature 
its vapor pressure is 0.4 ft. 


102 


CAVITATION AND ENTRANCE BUBBLES 



Figure 11. Chart showing relation between velocity, submergence, and cavitation parameter. 


VALUES OF CAVITATION PARAMETER. 


CAVITATION 


103 


tation void. Therefore each change in shape of the 
bubble produces corresponding changes both in the 
velocity and the pressure fields surrounding the body. 
Another way of saying this would be that each value 
of K corresponds to a given effective body shape. 
However, there is one unique characteristic of the 



B 

K = 0.54 


F 

K = a2« 


G 

K = 0.21 


Figure 12. Development of cavitation bubble. Hemi- 
spherical nose. This is an example of fine-grained cavita- 
tion. 

part of the effective body that is formed by the bub- 
ble. The original solid body was unaffected by a 
variation in pressure on it, i.e., the variation in pres- 
sure produced no change in the body shape. On the 
other hand, the bubble is incapable of resisting any 
appreciable difference in pressure over its surface. In 
other words, the pressure on the entire surface of 
the bubble must be uniform since in case it is not, the 


bubble will deform until it is. Thus the interface be- 
tween the bubble and the liquid is an isopiestic sur- 
face.® From this it might seem that if the pressure 
distribution around the body were measured or com- 
puted, the isopiestic surfaces would define the shape 
and course of growth of the cavitation bubble. This is 
not true because of the changes in the pressure fields 
produced by changes in the bubble shape. However, 
it is reasonable to suppose that for a given state of 
development of the cavitation bubble, the adjacent 
isopiestic surface in the flow will be a good indication 
of the direction of growth of the bubble as the 
pressure is lowered. 

Cavitation is often thought of as a very localized 
phenomenon which occurs in narrow zones such as 
those shown in Figures 12A and B. However, as seen 
in Figures 12C to G, if the pressure is reduced suffi- 
ciently, the cavitation grows to enormous propor- 
tions and may become many times the volume of the 
original body. This complete envelopment of a pro- 
jectile by a vapor or a gas bubble is easily possible if 
the velocity is high enough or if the pressure in the 
bubble is sufficiently great. Thus, in Figure 12G it is 
seen that only a portion of the hemispherical nose of 
the body is in contact with the water. The flow breaks 
away from the body before the full diameter of the 
projectile is reached. This is, of course, a typical 
bubble condition which occurs when the projectile 
enters the water from the air. 

^ ^ ® Types of Cavitation 

If a shape that has a relatively poor cavitation 
resistance such as a hemispherical nose, is studied, it 
will be observed that when cavitation commences it 
occurs in a sharply defined zone. It appears as a white 
band, which, upon closer examination, seems to be 
made up of a series of very small bubbles. As the 
pressure is lowered and the cavitation zone spreads, 
the zone remains quite sharply defined, especially at 
the leading edge, and the character of the surface 
stays approximately the same. This might be called 
“fine-grained cavitation.” A typical case of this type 
is seen in Figure 12. In contrast to this, if a shape hav- 
ing more cavitation resistance is subject to a similar 
scrutiny, as, for example, a long elliptical or more 
pointed nose, cavitation will appear first as a series of 
individual and comparatively large droplike bubbles. 

° This statement ignores the minute pressure gradient that 
may exist due to gas circulation in the bubble. This factor is 
discussed in Section 4.3.7. 


104 


CAVITATIOIN AND ENTRANCE BUBBLES 


As the pressure is reduced, these bubbles grow more 
numerous until they cover the entire surface, but 
they retain their individual character over a wide 
range of cavitation conditions. This we will term 
“coarse-grained cavitation.” A characteristic ex- 
ample of this class is seen in Figures 13A to C which 
show cavitation development on an ogive having a 
radius of curvature equal to 2.0 body diameters. 



Figure 13. Development of cavitation bubble. Two- 
caliber ogive nose. This is an example of coarse-grained 
cavitation. 


One possible explanation of the reason for the dif- 
ference in the appearance of these two variants of the 
cavitation phenomenon may be found in an exami- 
nation of the pressure distribution occuring on the 
two shapes. In the case of the hemispherical nose the 
pressure gradient is relatively steep, and therefore, 
the zone in which the pressure becomes equal to the 
vapor pressure is quite sharply defined. Consider two 
elements of liquid moving abreast in parallel paths 
along the body. Both enter the cavitation zone at the 
same instant so that there is no time available for the 


change in flow produced by the presence of the gas 
bubble formed in one element to affect the pressure, 
and hence the evolution of gas in the adjacent ele- 
ment. Therefore, cavitation occurs simultaneously in 
the two elements, and consequently around the en- 
tire circumference of the nose. On the other hand, on 
the long ogive nose, the pressure gradient is much 
smaller. Therefore, the exact point on the path of the 
liquid element at which the pressure reaches the 
vapor pressure is much less sharply defined. Thus, it 
is possible to imagine that, owing to localized fluctua- 
tions in velocity that are always present in turbulent 
flow, or possibly in some instances due to a minor 
surface imperfection, such as a scratch on the body, 
one element of the fluid would reach the vapor pres- 
sure slightly before the corresponding one on the 
neighboring parallel path. The resulting gas bubble 
would cause the liquid to be deflected around it, 
which might result in a slight increase in pressure on 
the liquid in the adjacent element and thus delay 
vaporization from it until it has moved a short dis- 
tance further downstream. This explanation is very 
tentative and is offered without any background of 
quantitative experimental confirmation. 

^ ^ ® Effect of Cavitation 

on Underwater Performance 

Comparatively little quantitative information is 
available about the effect of cavitation on the per- 
formance of underwater projectiles. The exceptions 
to this statement include (1) the case of propeller 
cavitation, since much study and analysis has gone 
into the investigation of the effect of cavitation on 
propeller performance, and (2) measurements of the 
forces on a group of cavitating projectiles. (See 
Chapter 5.) For further details reference should be 
made to the publications of the David Taylor Model 
Basin, the Department of Naval Architecture at the 
Massachusetts Institute of Technology, etc. 

The presence of the cavitation bubble on the main 
body of the projectile would be expected to modify 
the normal hydrodynamic forces of drag, cross force, 
and moment. The nature and magnitude of these 
effects are discussed together with those of the en- 
trance bubble in Section 4.5. However, there is one 
effect, probably peculiar to the inception of true 
cavitation, that will be mentioned here. There is 
some evidence to indicate, on certain body shapes, 
that there is a very small reduction in drag just be- 
fore or during the inception of cavitation. This re- 


CAVITATION 


105 


duction seems to be followed by a quite rapid in- 
crease in drag as the cavitation zone develops to an 
appreciable magnitude. If the normal division of the 
total drag into skin friction and form drag is con- 
sidered, it is not very difficult to find an explanation 
for this anomalous behavior. It would be expected 
that the presence of the cavitation bubble would 
affect the two components of the drag in opposite 
manners. The skin friction should be reduced, since 
the total area of the projectile exposed to the flow of 
the liquid is decreased. Furthermore, the first traces 
of cavitation may possibh^ inhibit the growth of the 
boundary layer. One would expect the form drag to 



Figure 14. Drag coefficient versus cavitation para- 
meter. 


increase, since it would be a rare case indeed in which 
the presence of the bubble could be expected to im- 
prove the hydrodynamic form of the body enough to 
overbalance the increase in drag which would result 
from the larger effective diameter due to the presence 
of the bubble. Through the interplay of these two 
opposing effects, it is possible that at the inception of 
cavitation, the skin friction is reduced more than the 
form drag is increased; whereas, as the cavitation 
develops, the increase in form drag overtakes and 
then completely masks the reduction of skin friction. 
Figure 14 gives the results of a drag test which shows 
this effect. 

^ ^ Gas Cycles in Cavitation 

In general, little attention has been paid to the be- 
havior of the vapor which Alls a cavitation bubble. 
For many purposes it has been adequate to consider 
the space as if it were a complete vacuum. Actually 
it is gas filled. That part of the surface which is 


bounded by the liquid is moving rapidly with re- 
spect to the gas. The gas is produced by vaporization 
of the liquid through this interface. Since the heat 
for this vaporization comes from the sensible heat of 
the liquid itself, the process must result in a decrease 
in temperature of the liquid. As the percentage of 
liquid that is vaporized must be extremely small, this 
decrease in temperature is probably negligible for any 
of the present considerations. It might be assumed 
that the downstream boundary of the cavitation 
zone is a region of condensation where the vapor 
collapses back to the liquid state. However, observa- 
tion of actual cavitation quickly shows that, although 
this may be partially true, it does not describe the 
phenomenon completely. The downstream end of the 
cavitation zone can be seen to be a region of very 
rapid entrainment of elements of the gas by the 
rapidly moving liquid. This is especially evident in 
photographs taken with very short-duration flash 
illumination. In such pictures it is possible to see not 
only clouds of minute bubbles being swept far down- 
stream from the end of the cavitation zone, but large 
individual bubbles can be observed in the process of 
entrainment and transportation downstream. All the 
cavitation photographs presented here are taken with 
such flashes which give a resulting exposure time be- 
tween 1 and 25 /xsec. Figure 15 shows this entrain- 
ment quite clearly. Furthermore, within the main 
cavitation bubble there must be a rather intense 
circulation of the gas, since a large part of the surface 
is formed by the moving liquid, which must induce a 
corresponding flow in the gas. Since all of this gas 
cannot be entrained at the downstream end, there 
must be a resulting forward counter flow along the 
surface of the projectile to complete the circulation, 
as shown on the sketch in Figure 16. It is probable 
that one result of this circulation pattern is that there 
is a minute pressure difference which exists between 
the upstream and downstream end of the bubble, the 
higher pressure being at the upstream end. 

The appearance of some of the well-advanced 
cavitation bubbles points to the existence of this gas 
circulation and pressure difference. Thus Figures 17A 
to D show the various stages in the development of 
cavitation on a projectile having a nose of low cavita- 
tion resistance. In the beginning the entire surface of 
the bubble appears milky or frothy and seems to be 
made up of a series of minute bubbles. It might be 
assumed that the entire space was filled with this 
froth. However, it must be remembered that rapid 
evaporation is taking place from the liquid through 


V T:o':\‘'(<n)K\'ri \r*) 


106 


CAVITATION AND ENTRANCE BUBBLES 



Figure 15. Entrainment from cavitation bubble. Flow velocity 60 feet per second. Interval between pictures approxi- 
mately 1/750 second. Note arrows showing beginning of second and third breaks. 




ENTRANCE AND C AVIT ATION BUBBLES 


107 


the interface into the gas space. The observer is 
looking from the liquid side and very probably sees 
only the breaking bubbles at the surface. Since the 
rate of entrainment at the downstream end of a 
cavitation zone is obviously high, the rate of vapori- 
zation is equally high in order to supply the required 



Figure 16. Gas circulation within bubl)le. 


amount of gas. However, as the surrounding pressure 
decreases and the size of the bubble increases, the 
amount of the surface through which vaporization 
can occur appears to increase more rapidly than the 
entrainment. This is shotvm by the fact that the for- 
ward part of the bubble begins to have glassy zones 
through which the projectile can be seen. As the 
bubble size increases further, this smoothing of the 
surface, i.e., the decrease in vaporization through it, 
spreads downstream until the entire length of the 
projectile is visible, as in the case of Figure 17D. Now*, 
if the pressure within the bubble were uniform, it 
wnuld be expected that the rate of vaporization 
wnuld be decreased uniformly over the whole inter- 
face. How ever, the photographs show’ that this is not 
the case and that the vaporization disappears first at 
the forward end of the bubble. The easiest explana- 
tion is the one previously offered, i.e., that the gas 
circulation has produced a slight pressure gradient 
wdth a higher pressure at the upstream end. 


* * ENTRANCE AND CAVITATION 
BUBBLES 

Similarities and Differences 

The discussion of entrance and cavitation bubbles 
at the beginning of this chapter and occasional refer- 
ences later on have indicated that the two phenomena 
belong to the same family. How’ever, it is con- 
structive to examine the specific points of similarity 
and difference betw’een them. 

If the tw'o bubbles are compared on the basis of the 
cavitation parameter K, it will be found that for the 
same value of A on a given projectile, the cavitation 


bubble and the entrance bubble will be of the same 
size and shape within reasonably close limits, i.e., 
they are geometrically alike. It must be remembered 
that in computing the value of K for the entrance 
bubble, the pressure of the air inside the bubble must 
be used for Pb, in place of the vapor pressure of the 
w’ater. As the air pressure is much higher than the 
vapor pressure, a given value of K is obtained at 



Figure 17. Development of cavitation on a blunt 
nose, showing transition to clear bubble. 


much lower velocity for an air-filled bubble than for a 
true cavitation bubble. Since the bubbles are similar, 
their effect on the drag coefficient and on the coeffi- 
cients of the other hydrodynamic forces should be the 
same. It should be noted that force coefficients are 
specified rather than the forces themselves because 
the velocities involved for the same values of K are 
quite different in the tw^o cases. 


108 


CAVITATION AND ENTRANCE BUBBLES 


The gas supplies for the two cases are quite dif- 
ferent. The cavitation bubble has an unlimited gas 
supply through the vaporization of the surrounding 
water, whereas the entrance bubble has a very limited 
supply. When a projectile enters the water from the 
air, the supply of air to the bubble is cut off when the 
air tube to the surface closes. Henceforth, as the gas 
is pumped away through entrainment at the down- 
stream end, either the bubble must get smaller or the 
pressure within it must drop. This process must con- 
tinue until the bubble is completely consumed. How- 
ever, for corresponding K’s the gas circulation and 
the entrainment should be comparable to that of the 
cavitation bubble. For the air bubble the interface 
will always be clear and transparent since no vapori- 
zation takes place across it. 

Under some conditions the cavitation bubble can 
be considered a steady-state phenomenon. For ex- 
ample, a projectile running at a constant depth and a 
constant velocity could maintain continuously a 
cavitation bubble corresponding to the existing value 
of K. The entrance bubble, on the other hand, is in- 
herently transient because it has no continuous sup- 
ply of gas. It is, of course, possible to imagine condi- 
tions on a torpedo in which the exhaust gases from 
the power plant could act as the source of supply. 
Likewise, the products of combustion from a jet- 
propelled torpedo might furnish sufficient gas to 
maintain an entrance bubble. However, it appears 
that for the normal projectile shapes and arrange- 
ments, these points of discharge are not very favor- 
able for the maintenance of the bubble. This is very 
fortunate, since it would be impossible to secure 
acceptable performance if a bubble large enough to 
envelop the body were maintained during the entire 
run. 

^ ^ ^ Entrance-Bubble Formation 

An examination of the cavitation parameter shows 
that at the point of passing through the interface, 
every projectile entering the water from the air is 
operating with a A of zero, since at that point Pl = 
Pb- Therefore, every projectile shape, no matter how 
excellent, must produce a bubble at water entrance. 
However, K rapidly assumes a finite value as the 
depth of submergence increases, even though an open 
passage is maintained from the projectile to the sur- 
face through which the air can continue to enter. This 
is because Pl always increases directly with the 
submergence. 


The entrance phenomenon starts when the pro- 
jectile first touches the water. From this point on and 
continuing during the first diameter or two of travel 
the change in the phenomenon is so rapid that it has 
no significant effect during the rest of the life of the 
bubble. The initial accelerations imparted to the 
water are very high, and in the case of oblique entry 
the forces on the projectile are asymmetrical. There- 
fore, during this beginning part of the phenomenon, 
there is probably little similarity between the be- 
havior of the entrance bubble and the bubble ob- 
served under steady-state conditions. However, the 
flow pattern rapidly becomes established and the 
rates of change of the conditions decrease so that 
soon the differences between the transient and 
steady-state conditions are not of major importance. 
Since this discussion is largely based on the results of 
experiments and analysis of steady-state conditions, 
the conclusions are inherently limited to this second 
phase of the entrance phenomenon. It would seem 
that as a rough approximation this second phase 
might be thought of as beginning at about the time 
the projectile has traveled three or four diameters 
from the point of contact. 

The entrance bubble is apparently formed for the 
same dynamic reasons that the cavitation bubble is 
formed. The water is forced out of the path of the 
moving projectile by the nose, thus giving the water a 
radial component of velocity. If the flow is to conform 
to the shape of the body, a point is soon reached when 
an acceleration must be produced towards the body. 
If the pressure difference between the fluid and the 
surface of the body is not sufficient to produce this 
acceleration, then the flow will not follow the body 
surface. If there is a supply of gas available, the 
intervening space will be filled by it. This is, of 
course, what happens when the projectile enters the 
water. The water is forced away from the projectile 
and at the surface there is no restoring force; hence, 
only the forward part of the projectile is in contact 
with the water and the bubble forms aft of this point. 
As the nose penetrates below the surface, the hydro- 
static pressure builds up and acts to restrict the size 
of the bubble. It should be noted that the only force 
acting outward away from the projectile is supplied 
by the wetted portion of the nose. From this zone aft, 
all the forces act to produce an acceleration toward 
the body, thus tending to decrease and later to re- 
verse the outward radial velocity component. If the 
velocity of entrance is low, it is possible for the hydro- 
static forces to close the bubble either on the mid- or 


PROJECTILE DYNAMICS IN CAVITATION, ENTRANCE BUBBLES 


109 


after-section of the projectile. However, if the en- 
trance velocity is increased, the hydrostatic forces 
will require a longer time to close the bubble. In this 
case the length of the bubble will be increased due to 
two factors, (1) the bubble is open longer and (2) the 
projectile is going faster, thus creating greater length 
per unit time. Since the forces at the surface tending 
to cause closure are very low, closure will normally 
take place at some point below the surface. Then a 
residual tube of air from the point of closure to the 
surface will be expelled, causing considerable surface 
disturbance. 

From the point of view of the above analysis, it 
mil be seen that the maximum diameter of the en- 
trance bubble for a given trajectory angle will depend 
upon two factors, (1) the shape of the nose and (2) 
the speed of the projectile. These control the magni- 
tude of the outward acceleration and hence the size 
of the bubble, since the restoring force, i.e., the sub- 
mergence, is constant. 

^ ^ ^ Bubble Decay 

The mass of air present in the entrance bubble 
reaches a maximum at the instant of its closure. From 
that point on, the bubble steadily loses air to the 
surrounding liquid. In discussing the gas cycle within 
the cavitation bubble, it was pointed out that the 
downstream end of the bubble is a region of very 
rapid entrainment of the gas. This is equally true of 
the entrance bubble. The surrounding water acts as 
an ejector to pump the air out of the bubble by 
breaking off or entraining its elements. Thus, the 
mass of gas continues to decrease. The volume of the 
bubble, however, is determined not only by the mass 
of the gas within it, but also by the pressure at which 
this mass is at equilibrium with its motion relative to 
the liquid. This pressure, in turn, is a function both 
of the velocity of the projectile and the submergence, 
and, in addition, is affected by the shape of the nose. 
In short, it is governed by the value of K, just as was 
the case when the bubble was filled with water vapor. 
It will be seen that, if a projectile is submerged and 
running with constant velocity at constant depth 
within an entrance bubble, as the air is pumped out of 
the bubble Pb will decrease and hence the value ofi^ 
will increase until the bubble disappears. This state- 
ment assumes further that, at the time that the last 
trace of air is entrained, the value of K is greater than 
the K for incipient cavitation. If this is not the case, 
the water will vaporize and the bubble will gradually 


turn into a pure cavitation bubble in which the void 
is filled entirely by water vapor. In the case of high- 
speed entry, it is very probable that this actually 
occurs, i.e., that the air-filled entrance bubble merges 
gradually into the vapor-filled cavitation bubble be- 
fore the velocity is reduced sufficiently to eliminate 
the cavitation. Such a condition would be more apt 
to occur on a shallow-diving than on a deep-diving 
projectile, since, for similar velocity conditions, the 
latter projectile has a higher K. 

If it is assumed that the projectile under considera- 
tion either is without power or is driven by propellers, 
the entrance bubble phase of the trajectory will be 
one of continually decreasing axial velocity. This de- 
crease, in effect, acts as a compressing force on the 
air-filled bubble since it is tending to raise the value 
of K, and hence, to decrease the size of the bubble. 
If the submergence is increasing at the same time, 
this effect is accelerated. This compression alone 
probably tends to increase the mass rate at which the 
gas is pumped out of the bubble, simply because there 
is more mass carried away in a given volume of gas. 


4 5 PROJECTILE DYNAMICS 

WITHIN CAVITATION 
AND ENTRANCE BUBBLES 

A certain superficial similarity exists between the 
forces acting on underwater projectiles when en- 
veloped in a bubble and the air flight of a similar 
projectile traveling at supersonic velocities. In both 
cases, assuming zero yaw, the principal force acts on 
the nose alone, and in general its point of application 
is well ahead of the center of gravity. Furthermore, in 
both cases the nose shape is of prime importance in 
determining the magnitude of the force for a given 
velocity. However, there is little point in pursuing 
this similarity very far since the mechanics of the two 
phenomena are quite different. 

The forces on the projectile within the bubble are, 
as in the case for any other portion of the path, the 
result of the reaction from the change in momentum 
produced in the surrounding fluid by the presence of 
the projectile. Thus, if the movement of the water 
surrounding the projectile and its bubble were known, 
the projectile forces could be calculated. Since the 
surface of the bubble defines the path of the adjacent 
layer of water, the bubble shape can be used as an 
indication of the character of the flow. Since a change 
in the force on the projectile is the result of a change 




110 


CAVITATION AND ENTRANCE BUBBLES 


in the momentum imparted to the water by the pro- 
jectile, such a change must be accompanied by a 
change in the bubble shape, i.e., in the path of the 
water adjacent to the bubble. Investigations^ of the 
performance of a certain special type of underwater 
projectile for Division 3 have led to the hypothesis 
that the bubble diameter at a given distance back of 
the head is an effective measure of the drag on the 
projectile, the force varying roughly as the diameter 
to the fourth power. This hypothesis assumes that the 
skin friction is negligible, since the wetted surface 
area is negligible, and that the drag force is directly 




B drag and cross force components on 

PROJECTILE NOSE AND TAIL WHEN TAIL 
TOUCHES CAVITY WALL 

Figure 18. Projectile with yaw in entrance bubble. 

proportional to the radial force imparted to the water 
to get it out of the way of the projectile. This latter 
statement implies a constant “efficiency’’ of the nose 
as a deflector, or in other words, all noses producing 
the same diameter of bubble are acted upon by the 
same force. This is probably true only within reason- 
able limits. For example, it would seem that in the 
case of a square nose, part of the axial force might be 
used to impart an appreciable axial component of 
velocity to the water; whereas a long ogive, or fine 
ellipse, might produce the same diameter bubble, but 
would impart practically no axial velocity to the 
liquid. For detailed measurements of the drag and 
other forces acting on a few specific body shapes, see 
Chapter 5. 

* ® ^ Cross Force in Bubble 

In the preceding paragraph, the shape of the bub- 
ble was used as a basis for some of the conclusions 
regarding the drag. Bubble shape is equally helpful in 
the investigation of the cross force. Thus, if the bub- 


ble is symmetrical, it is reasonable to suppose that 
the resultant force acts along the axis of symmetry of 
the bubble. If the axis of symmetry of the bubble 
coincides with the trajectory there should be no re- 
sultant cross force on the projectile. If the axis of the 
bubble makes an angle with the trajectory, then a 
cross force should be expected and its magnitude 
should be about equal to the drag force multiplied by 
the sine of the angle between the axes. In most cases, 
however, it will be observed that when the axis of the 
bubble does not coincide with the trajectory, the 
bubble is asymmetrical. For this case the bubble axis 
is not significant, so the resultant force must be used. 
Its line of action is determined by the condition that 
in any plane containing this line, the amount of mo- 
mentum change in this plane must be equal and 
opposite on each side of the line of action. 


4.5.2 Equilibrium Yaw Angles 

within Enveloping Bubbles , 

Figure 18 is a diagrammatic sketch of the condi- 
tions which exist when a projectile is surrounded with 
a bubble, and is traveling with a pitch or yaw with 
respect to its trajectory. In the preceding paragraph 
it was pointed out that the cross force on a projectile 
is a function both of the force resisting the motion 
and the angle that the force makes with the trajec- 
tory. It will be seen from Figure 18A that this angle 
can be defined by two others: (1) the pitch or yaw 
angle of the projectile with the trajectory, and (2) the 
inclination of the bubble axis or line of action with the 
projectile axis. It should be remembered in comput- 
ing the cross force that the accepted definition is that 
the cross force is normal and the drag force is parallel 
to the trajectory, regardless of the angle between the 
projectile axis and the trajectory. 

Some further simple deductions can be made con- 
cerning the forces acting on the projectile while it is 
surrounded by the bubble. 

1. The forces can act only on those portions of the 
projectile that are in contact with the water. There- 
fore, it is obvious that the moment produced by the 
hydrodynamic forces on the nose is usually a de- 
stabilizing one, since its point of application is al- 
ways ahead of the center of gravity. Thus, unless the 
line of action of the nose force makes a greater angle 
with the trajectory than does the axis of the pro- 
jectile, the resulting moment will be in a direction to 
increase the yaw. 


CHARACTERISTICS OF SPECIFIC NOSE SHAPES 


111 


2. If continuous rotation of the projectile is to be 
prevented, a moment of equal and opposite magni- 
tude must be applied. The forces which can produce 
such a moment first come into play when other points 
of the projectile touch the bubble interface. In pro- 
jectiles of normaTshapes the afterbody and the tail 
structure will be the points that will touch first. 
Since such points of contact lie well aft of the center 
of gravity, as shown in Figure 18B, the moments re- 
sulting from the forces applied at these points are 
stabilizing. 

3. If the stabilizing moment from these forces in- 
creases faster with increasing yaw than does the de- 
stabilizing one from the nose force, an equilibrium 
yaw angle can be reached at which these two mo- 
ments will be balanced. Since under these conditions 
the cross forces will not balance, the projectile will be 
forced into a curved path. If this condition persists 
long enough to obtain equilibrium, the radius of 
curvature of the path will be such that the cen- 
trifugal force just balances the hydrodynamic cross 
force. 


* ® * Relation between Size of Bubble 
and Equilibrium Yaw Angle 

Some qualitative conclusions can be drawn con- 
cerning the interaction between the various parts of 
the projectile. 

1. Other things being equal, the curvature of the 
path will depend upon the magnitude of the cross 
force. 

2. For a given nose and location of center of 
gravity, the cross force will depend on the equilibrium 
angle of yaw and the distance aft from the center of 
gravity to the points at which the forces that furnish 
the stabilizing moment are applied. 

3. From this it follows that the longer the after- 
body and the larger the diameter of the tail structure, 
the greater will be the radius of curvature, or, in 
other words, the less will be the deviation of the 
projectile from a straight path. The reasoning is as 
follows: The bubble size and shape is a function of 
the nose shape alone. Therefore, for a yawing pro- 
jectile, the farther aft the afterbody and tail struc- 
ture extends from the center of gravity, the sooner 
they will come in contact with the wall of the bubble. 
Thus, the longer the afterbody and tail, the smaller 
will be the equilibrium angle and the less will be the 
cross force on the nose. Furthermore, the amount of 


tail cross force required to produce the necessary 
stabilizing moment will decrease as the points of con- 
tact of the afterbody and tail move aft. 

4. The same line of reasoning leads to the state- 
ment that the radius of curvature of the path of a 
projectile of given construction can be changed 
simply by changing the shape of the nose. Two fac- 
tors enter into this: the size of the bubble produced 
and the amount of cross force for a given yaw. Thus, 
if a change in the nose is made which results in a 
larger bubble but leaves the relationship between 
cross force and yaw unchanged, the effective cross 
force at equilibrium will, nevertheless, increase. This 
is because the projectile will have to rotate to a larger 
yaw angle before the afterbody and tail come in 
contact with the bubble surface and are forced into 
it far enough to develop the moment required to 
balance the destabilizing moment of the nose. This 
larger yaw angle means a greater cross force on the 
nose as well as a greater cross force on the tail, and 
hence, a shorter radius of curvature to produce the 
centrifugal force required to balance this larger cross 
force. The result would be the same if the nose were 
changed in such a manner that the size and shape of 
the bubble would be unaffected, but that the result- 
ing cross force would be larger for a given yaw angle. 
In general, it is very difficult to modify the bubble 
shape without affecting the cross force and vice versa, 
since, as previously pointed out, the bubble shape 
and the nose forces are intimately related. 

5. It will be seen from the interrelation of these 
factors that any change in the design of a given pro- 
jectile that affects the shape of the nose, the shape of 
the afterbody and tail surfaces, or the position of the 
center of gravity, will result in a change in the per- 
formance of the projectile while it is in the bubble. 
Conversely, when the relative behaviors of these 
various factors are known and understood, it may be 
possible to design a projectile with any desired be- 
havior in the bubble phase. 


*6 CHARACTERISTICS 

OF SPECIFIC NOSE SHAPES 

Chapter 5 contains a discussion of the detailed 
characteristics of a group of specific nose shapes, and 
Chapter 6 presents measurements of the forces act- 
ing on projectile bodies when operating under various 
stages of cavitation. The present discussion will be 
limited to a few general comments on the significance 


112 


CAVITATION AND ENTRANCE BUBBLES 


of nose cavitation with respect to the behavior of the is zero and the moment is directly proportional to the 
projectile. yaw. 


Hemispherical Noses 


Ellipsoidal Noses 


If the bubble produced by a hemispherical nose is 
observed from its inception until it develops to a 
length of many times that of the projectile, it will be 
seen that when it first appears it is located nearly at 
the junction between the hemisphere and the cylin- 
der. As it grows longer and longer, the point at which 
it springs clear from the nose slowly moves forward 
until, when the bubble is fully developed, it leaves the 
hemisphere considerably forward of the point of 
tangency of the sphere with the cylinder. This is 


A 

YAW =0° 
K = 0.22 


B 

YAW= y 
K = 0.22 


C 

YAW =6" 
K = 0.23 


Figure 19. Cavitation. Hemispherical nose. Yaw 0, 

3, and 6 degrees. 

clearly shown in Figure 12. If, when the bubble is 
fully developed, the projectile within it is yawed a 
few degrees, the shape of the surface in contact with 
the water is unaltered since it always remains a seg- 
ment of a sphere. Figures 19A to C show this be- 
havior. Note especially that the line of contact of the 
bubble with the projectile nose always remains per- 
pendicular to the direction of flow, that is, to the tra- 
jectory. This property of preserving the same con- 
tact surface, independent of the pitch or yaw angle, 
is unique to the sphere. The result is that the bubble 
is unaffected in shape or alignment with the tra- 
jectory by moderate pitches or yaws, and conse- 
quently, the resultant force on the projectile is un- 
changed in magnitude and direction with respect to 
the trajectory. Hence, for small angles the cross force 



If the development of the bubble on a projectile 
with an ellipsoidal nose is observed in the manner 
just described, it will be seen that the superficial be- 
havior is similar, i.e., as the bubble grows, its point 
of contact moves forward on the nose. However, in 



Figure 20. Development of cavitation; 2-to-l ellip- 
soidal nose. 


the case of the ellipsoid, the amount of forward move- 
ment is considerably greater than that on the hemi- 
sphere. This movement can be observed in Figure 20. 
If, while the bubble is fully developed, the projectile 
is again yawed slightly, it will be seen that the wetted 
surface becomes asymmetrical and causes the bubble 
to alter its shape and alignment. This change ap- 
pears to be in the direction to increase the cross force 
and the moment, largely as the result of swinging the 
axis of the bubble. Figure 21 shows top views of fully 
developed cavitation on the nose shape shown in 


CHARACTERISTICS OF SPECIFIC NOSE SHAPES 


113 


Figure 20, comparing the bubble shapes with and 
without yaw. Note particularly that with the ellipti- 
cal nose, the line of contact of the bubble mth the 
projectile swings from perpendicular to the flow at 



Figure 21. Full cavitation with yaw, 2-to-l ellipsoidal 
nose. Top view. 


zero yaw, to a deviation from perpendicular of from 
two to three times the yaw at 6 degrees, and that this 
rotation is in the opposite direction to that of the 
yaw. 


tation follows the laws of geometrical similarity. 
This means that the radius of curvature must be 
measured in relative rather than in absolute units, 
i.e., in calibers or diameters of the body. For simple 
shapes, such as ogives and ellipsoids, the greater the 
radius of curvature at the point of tangency, the 
higher will be the cavitation resistance, i.e., the lower 
will be the parameter K at the inception of cavita- 
tion. Figure 22 shows the results of the experimental 
determination of K for inception on various ellipsoids 
and ogives. It should be noted that although these 
two series of shapes look quite different, the K’s are 
about the same for equal curvatures at the point of 
tangency. 



RADIUS OF CURVATURE AT POINT OF TANGENCY, CAUSERS 


Figure 22. Cavitation parameter, K*, versus curva- 
ture. 


Ogives 

The behavior of simple ogives, i.e., nose shapes 
generated by the rotation of an arc of a circle which 
is tangent to the cylinder, is about the same as that 
of the family of ellipsoids. Other nose shapes which 
are finer than the hemisphere have a similar type of 
behavior, i.e., finite cross forces exist even at small 
yaws and both cross force and moment increase 
more rapidly with fsiw than they do with the 
hemisphere. 

^ ® ^ Resistance of Noses 

to Inception of Cavitation 

The resistance of many nose designs to the incep- 
tion of cavitation appears to depend upon the radius 
of curvature of the nose at the point of tangency with 
the cylindrical portion of the body. Apparently, cavi- 


* ® ® Entrance Bubble and Cavitation 
Performance Characteristics 
for Successful Overall Flight 

In much of the previous discussion very little at- 
tempt has been made to distinguish between the 
characteristics of the entrance and the cavitation 
bubbles. The primary reason for this lack of distinc- 
tion is, of course, that they are felt to be two aspects 
of the same phenomenon. However, in considering 
the overall trajectory, it must be remembered that 
generally speaking, if both manifestations occur, 
they are not concurrent, but appear one after the 
other. Therefore, it is necessary to examine the pro- 
jectile shape from two separate viewpoints, i.e., to 
see if it will give satisfactory performance (1) in the 
entrance bubble and (2) in the subsequent under- 
water run. 


114 


CAVITATION AND ENTRANCE BUBBLES 


SPEED 

KNOTS ? y 40 50 60 7y 80 30 100 


FT/c;Fr. 40 fin ro inn i?n i/in tfin ifin 




F iGUKE 23. Hemispherical nose. Cavitation development related to depth and speed. 



CHARACTERISTICS OF SPECIFIC NOSE SHAPES 


115 


At first sight it might appear that the best en- 
trance bubble would be none at all. However, the 
previous discussion has shown that at the water sur- 
face every nose shape will form an entrance bubble; 
that it is very difficult to design the nose so that at a 
given speed this bubble will be exactly the size of the 
projectile; and that even if this were achieved for one 
speed, the bubble would be longer and larger as the 
speed was increased. Furthermore, the entrance 
bubble may serve the very useful purpose of increas- 
ing the curvature of the path in the vertical plane so 
as to reduce the maximum depth of dive and shorten 
the distance from the point of entrance to the begin- 
ning of the normal part of the run. Satisfactory per- 
formance in the bubble phase must include the 
following items: 

1. The decelerating force, and hence, the drag in 
the bubble, must be kept below the point at which 
structural damage occurs. 

2. The projectile must remain on course in the 
horizontal plane. 

3. The combination of the cross force and the pitch 
in the bubble must result in a curvature which pre- 
vents deep dives, but does not permit the projectile 
to “broach.” 

The most desirable cavitation characteristic for a 
torpedo or similar projectile is that cavitation does 
not occur on any part of it during its normal steady- 
state run. If this is impossible to achieve, then for 
satisfactory performance to be obtained, the cavita- 
tion effects must staj^ within the following limitations : 

1. The drag must not be increased appreciably. 

2. The change in the cross force and moment must 
not affect the stability adversely. 

3. The cavitation must not blanket or reduce 
appreciably the effect of the control surfaces. 


4. The propulsive efficiency must not be reduced. 
These limitations mean essentially that if cavita- 
tion does occur, it must be extremely limited, especi- 
ally in the regions of the control surfaces and pro- 
pellers. 

^ ® ® Selection of Nose Shape 

for Satisfactory Overall Performance 

A review of the discussion of the effect of nose 
shape on the performance within the entrance bubble 



Figure 24. Family of 5-caliber spherogives. Cavita- 
tion parameter, Ki, versus angle of sphere. 


indicates that, in general, the fine noses, such as long 
ellipsoids and ogives, produce such high cross forces 
that the projectile is very hard to control while in the 
bubble, is liable to broach badly, and on the other 
hand, may make deep dives if at the water-entry 
point there is an appreciable down pitch. These un- 
desirable characteristics may be alleviated by in- 
creasing the effective length of the projectile, either 



Figure 25. Family of 5-caliber spherogives. 

^\FU)KNTI^I. j 


116 


CAVITATION AND ENTRANCE BUBBLES 


by actually lengthening the body or by applying a 
shroud ring to the tail. However, hemispherical or 


e» 4 CENTRAL ANGLE 
OF SPHERE 



e » 86 

K » 0.57 


Figure 26. Family of 5-caliber spherogives cavitation 
photographs. 

*‘near’’ hemispherical noses show more desirable 
entry characteristics, particularly for small entry 


angles. Further improvement appears possible by 
using even blunter shapes. On the cavitation side of 
the picture conditions are exactly the reverse. The 
finer the nose, the better the cavitation resistance. 
It will be seen from Figure 23 that cavitation begins 
to appear on the hemispherical nose at 50 knots and 
40-ft submergence, and increases rapidly if either the 
speed is increased or the submergence decreased. 
Blunter noses show even poorer performance. It is 
obvious that the hemispherical nose is not satis- 
factory for a modern high-speed torpedo, and it can 
be anticipated that future requirements will call for 
even higher speeds and lower minimum submergences. 
It thus appears that the nose shape requirements 
for satisfactory performance within the entrance 
bubble and satisfactory cavitation performance 
during the normal run are diametrically opposed. 

^ ® Spherogive Noses 

One promising approach to the problem of satisfy- 
ing simultaneously these conflicting requirements has 
been made. This is in the development of the so- 
called spherogive nose, a nose shape which consists 
of a tip formed by a segment of a sphere and a transi- 
tion section which consists of a single-radius ogive 
tangent to the sphere and to the cylindrical section of 
the projectile. This shape was investigated first to see 
if it offered a simple substitute for an ellipsoid. How- 
ever, a series of measurements showed that it pos- 
sessed some unique cavitation characteristics. For 
example. Figure 24 shows the performance of a 
family of spherogives constructed in accordance with 
the outline drawing of Figure 25. It will be seen that 
in the entire family the transition ogive has a con- 
stant radius. The only difference occurs in the radius 
and angle of the spherical segment which forms the 
tip. It will be observed that from the viewpoint of 
cavitation resistance as measured by the K for in- 
cipient cavitation, there is no significant difference 
between performance of the simple pointed ogive and 
all of the spherogives in this particular family in 
which the spherical tip has a half angle of 72 degrees 
or less. However, when the half angle of the spherical 
tip exceeds 72 degrees, the cavitation resistance con- 
tinues to decrease, reaching the value of the hemi- 
sphere when the central angle is 90 degrees. Figure 26 
shows the appearance of these various noses while 
cavitating. For all of the series with tips smaller than 
72 degrees, cavitation starts at the point of tangency 
with the ogive of the cylinder. For all the members 


CONFIDENTIAL 



CHARACTERISTICS OF SPECIFIC NOSE SHAPES 


117 


having spherical tips larger than 72 degrees, cavita- 
tion starts on the sphere, whereas, for the member 
having the spherical tip of 72 degrees, cavitation 
appears simultaneously on the sphere and at the 
point of tangency with the cylinder. One further item 
should be noted. All of the members of the series had 
better cavitation resistances than the hemisphere, and 
all of those having tips of 77 degrees or less had very 
good cavitation resistance. For example, they could 
all operate without cavitating under such severe con- 
ditions as a speed of 50 knots and 10-ft submergence. 

Reference to the discussion concerning the charac- 
teristics of the hemispherical nose in the cavitation 
bubble shows that its good performance is attributed 
to the fact that the line of action of the force with 
respect to the flow was unaffected by small angles of 
pitch or yaw, because the shape of the nose in contact 
with the water, and hence, the shape of the bubble 
was unaltered by the change in angle. Thus it would 
appear possible for a properly designed spher ogive to 
have good performance both within the entrance 
bubble and also during the subsequent steady-state 
running conditions. In the series under discussion, 
spherogives having tip angles between 72 degrees and 
77 degrees would seem to offer good possibilities, 
since the cavitation bubble, and hence, the entrance 
bubble, always leaves the nose from a point on the 
spherical tip. Under these conditions the projectile 
should be insensitive to pitch and yaw; whereas for 
steady-state running conditions there should be no 
cavitation on the nose for any speed below 50 knots 
at submergence greater than 10 ft. 


One further physical factor must be considered. If 
the projectile is to be insensitive to yaw or pitch while 
in the entrance bubble, the bubble must be large 
enough so that it does not touch the body of the pro- 
jectile at any point, after leaving the spherical tip, 
until it reaches the afterbody or the tail. This means 
that the bubble produced by the spherical tip must 
have a diameter larger than that of the projectile. 
A spherogive tip can be so designed that cavitation 
starts on the sphere, but that the sphere is so small 
that the bubble produced by it will not be so large as 
the diameter of the projectile. Hence, the bubble will 
touch on the ogive part of the nose and thus be 
opened out to an adequate diameter. If this happens, 
the insensitivity to yaw is forfeited. 

It is, of course, realized that the spherogive is 
probably not the best shape that can be constructed 
to satisfy the conflicting requirements of the en- 
trance-bubble and the cavitation characteristics. The 
ogive section can be improved, for example, by sub- 
stituting a curve of continuously changing curvature 
which has infinite curvature at the point of tangency 
with the cylinder. Improved characteristics may also 
be obtained by modifying the spherical tip to produce 
even less change in moment with pitch or yaw. How- 
ever, the basic principle involved, that of securing a 
good cavitation resistance by making the overall 
shape of the nose effectively fine, while designing the 
forepart so that the wetted surface at the head of the 
bubble has the correct shape for satisfactory bubble 
performance, seems to hold much promise for future 
developments. 



Chapter 5 

NOSE CAVITATION— OGIVES AND SPHEROGIVES 


51 INTRODUCTION 

T his chapter covers the progress of an investiga- 
tion of cavitation on various projectile nose 
shapes. It is apparent that a very extensive series of 
tests will have to be made in order to cover the 
ground in a satisfactory manner. Only the tests of 
ogive and spherogive noses will be described. A total 
of about fifty models of these two types of nose 
shape have been tested. However, all data in this 
chapter must be considered as preliminary only and 
subject to corrections based on future tests. The 
work so far done has furnished a fairly comprehensive 
overall picture of the performance of these two 
types of nose, even though the test data are rather 
meager. 

In order to obtain consistent results, it has been 
found necessary to make the models to very close tol- 
erances. All linear dimensions are held within ±0.001 
in. Especial care is exercised to be certain that the 
curves forming the nose are truly tangent and match 
within 0.001 in. or less. The angle of the spherical seg- 
ment forming the tip of a spherogive nose must be 
held to within a quarter of a degree as, in some cases, 
a variation of 1 degree will cause a change of 15 per 
cent in the value of the cavitation parameter. 


5 2 METHOD OF TEST 

One of the primary objects of the investigation was 
to determine the point of incipient cavitation for the 
various nose shapes. This was done by mounting the 
model in the high-speed water tunnel and observing 
the first evidence of cavitation as the pressure in the 
tunnel was lowered. The water velocity during these 
tests was, in general, held at a constant value of ap- 
proximately 60 fps. The cavitation parameter K, for 
the point of incipient cavitation, is calculated from 
the velocity and pressure in the tunnel as described in 
Chapter 4. This value of K for incipient cavitation 
will, hereafter, have the symbol Ki. 

After the point of incipient cavitation had been de- 
termined, the pressure in the tunnel was lowered, cor- 
responding to decreasing values of the cavitation par- 
ameter, and high-speed photographs were taken of 


the development of the cavitation bubble. These pho- 
tographs, which furnish valuable data regarding the 
nature, location, and extent of the cavitation effects 
for each nose shape, appear throughout this chapter 
and are discussed in the test. 


5 2 OGIVE NOSES 

Sixteen ogive nose shapes of different proportions 
have been investigated. The ogive nose profile is 
formed by two equal arcs tangent to the cylindrical 
portion of the projectile and meeting at a point. Fig- 
ure 1 is a drawing of the family of 16 ogive noses that 
were tested. The radii of these ogives varied from 0.5 
to 8.12 calibers, a caliber being the maximum diam- 
meter of the projectile. 

In Table 1 are given the observed values of K for 
incipient cavitation for the ogive noses, and these 
values are plotted in Figure 2. From the smooth 
curve in Figure 2, the value of Ki for each ogive has 
been determined and is shown in Table 1 . These lat- 
ter values will be referred to throughout this chapter 
as the K’s for incipient cavitation for ogive noses. 
The values of Ki can also be plotted against the 
curvature (1 /radius) of the ogive. Figure 3 shows 
this curve in which the values of Ki have been taken 
from the smooth curve of Figure 2. 


Table 1. Incipient cavitation parameter Ki for ogive 
noses. 


Ogive radius r 
in calibers 

Curvature = 
1/r in calibers 

Observed Ki Ki 

from Fig. 2 

0.5 

2.0 

0.75 

0.75 

0.625 

1.60 

0.61 

0.60 

0.75 

1.33 

0.53 

0.52 

0.875 

1.14 

0.46 

0.46 

1.0 

1.00 

0.40 

0.43 

1.125 

0.89 

0.40 

0.41 

1.25 

0.80 

0.39 

0.39 

1.50 

0.67 

0.37 

0.37 

1.75 

0.57 

0.37 

0.35 

2.0 

0.50 

0.34 

0.33 

2.5 

0.40 

0.31 

0.30 

3.0 

0.33 

0.27 

0.28 

3.875 

0.26 

0.26 

0.25 

4.5 

0.22 

0.21 

0.24 

5.0 

0.20 

0.21 

0.22 

8.12 

0.12 

0.17 

0.17 


118 


CONFIDENTIAL 


BUBBLE LOCATION 


119 



Figure 1. Family of ogives. 


The curve in Figure 2 indicates that there is a rapid 
decrease in K for incipient cavitation, as the ogive 
radius increases from 0.5 caliber (the hemisphere) to 
about 1.0 caliber, and from this point the value of Ki 
is much less affected by an increase in the radius. 

5 * OGIVE CAVITATION PHOTOGRAPHS 

The series of photographs in Figure 4 shows how 
the size of the cavitation bubble varies with different 
ogive shapes. These were selected to have practically 
the same value of K so the change in bubble size is 
due almost entirely to the nose shape. As would be 



Figure 2. Ogive radius versus cavitation parameter. 


expected, the more blunt the nose, the greater the 
cavitation effect. 

Figure 5 shows a series of cavitation photographs 
similar to Figure 4 but for a lower value of K and 
longer radius ogives. In this series also is seen the de- 
crease in cavitation effect due to decreasing bluntness 
of the nose. 

Figure 6 shows the development of the cavitation 
bubble on a 2.0-caliber ogive as the value of K is re- 
duced from 0.31 to 0.18. As the K for incipient cavi- 


tation for this nose is 0.33, the first picture shows 
about the least amount of cavitation bubble that can 
be photographed. In the last picture the bubble is 
quite well developed, although it has not by any 
means reached the proportions of a “full bubble. 
These pictures illustrate what has been termed 
“coarse-grained cavitation,” in which the cavitation 
bubble as a whole is made up of a multiplicity of fairly 
large individual bubbles. It is seen in this series that 
this formation persists throughout the various degrees 
of cavitation. 



Figure 3. Cavitation parameter versus curvature. 
Ogive noses. 


55 BUBBLE LOCATION 

Photographs of the various ogive noses were meas- 
ured in order to determine the location of the well- 
developed cavitation bubble. Measurements were 
made from the tip of the nose to the forward edge of 
the bubble, and the results are plotted in P4gure 7. 
With very few exceptions these measurements show a 
steady increase in the distance from the point of 
tangency of the ogive curve and the cylinder, to the 
forward edge of the bubble as the ogive radius in- 
creases. Measurements of the angle between the axis 
of the nose and the radius drawn to the forward edge 
of the bubble showed that this remained practically 
constant at 86 degrees. The measured values of this 
angle are plotted in Figure 8. 


120 


NOSE CAVITATION— OGIVES AND SPHEROGIVES 


56 HEMISPHERICAL NOSE 

The hemispherical nose is the limiting case of an 
ogive nose with minimum radius. It is interesting to 
compare the development of the bubble on this nose 
with that of the 2.0-caliber ogive just discussed. Fig- 
ure 12 of Chapter 4 shows the development of cavi- 
tation on a hemispherical nose with values of K rang- 
ing from 0.71 to 0.21, incipient cavitation on this nose 
occurring at a value of AT,: = 0.75. In this series of 
pictures it is seen that the cavitation bubble is of a 


different type, termed “fine-grained cavitation.’’ The 
cavitation effect begins as a band of very fine bubbles 
having a homogeneous appearance, a form which per- 
sists throughout the development of the bubble 
proper. 

5 7 TRANSITION ZONE 

It has already been pointed out that the curve of K 
for incipient cavitation plotted against ogive radius 
shows a rather abrupt change in slope in the region of 



Figure 4. Variation in cavitation developed on various ogives at Ki = approximately 0.26. (Note that longer ogives ex- 
tended to the right outside the camera range and appear cut off in these and subsequent photographs.) 


TRANSITIOJN ZONE 


121 


A 

1.5 CAL 
K= 0.19 


C 

2.0 CAL 
K= 0.18 


E 

3.875 CAL 
K= 0.19 








B 

1.75 CAL 
K= 0.18 



D 

3.0 CAL 
K = 0.20 


F 

4.5 CAL 
K=0.I9 


Figure 5. Variation in cavitation developed on various ogives at K = approximately 0.19, 



c 

K= 0.18 


B 

K=0.25 


K=0.3I 


Figure 6, Development of bubble; 2.0-caliber ogive. 


o 

O (/) 

o o 


90 

80 

70 

60 

50 

40 


f . 




! 

! 

! 1 ' 















AVEI 

RAGE = 

86“ 

















ANGL 

PHC 

E MEA< 
ITOGRAI 

5URED ( 
»HS SI 

ON 

lOWING 






A WELL DEVELOPED 
CAVITATION BUBBLE. 

1 1 1 


2 3 4 5 6 7 

RADIUS OF OGIVE, r, CAUBERS 


Figure 8. Angle to forward edge of well-developed 
cavitation bubble, ogive noses. 


1.0-caliber radius. It is interesting and probably sig- 
nificant to note that the type of cavitation bubble 
also undergoes a change in this region. Noses of less 
than 1.0-caliber radius show a distinct fine-grained 
cavitation bubble, and those of greater radii than 1.0 
caliber have a coarse-grained bubble. 



Figure 7. Distance of cavitation from tip of nose for 
well -developed bubble on ogive noses. 


122 


NOSE CAVITATION— OGIVES AND SPHEROGIVES 


Figure 9 shows pictures of three ogive noses having 
radii of 0.875, 1.00, and 1.125 calibers at three stages 
of cavitation, roughly for K’s of 0.40, 0.33, and 0.26. 
In the 0.875 series (A, B, and C), it is seen that the 
cavitation is of the fine-grained nature throughout, 
although some of the coarse-grained bubbles are 


appearing at the lowest value of K. The 1.0-caliber 
series, (D, E, and F), shows the typical fine-grained 
cavitation band at the highest value of K (D), and 
somewhat of a mixture of fine and coarse grain in E 
and F. The 1.125-caliber series, (G, H, and I), shows 
the typical coarse grain throughout. 



1.125 CAL OGIVE 


Figure 9. Influence of nose shape on formation of fine-grained and coarse-grained cavitation at different K values. 


EFFECT OF YAW 


123 


5 8 EFFECT OF YAW 

It is intended to investigate the effect of yaw on 
the cavitation bubble for the full range of noses in- 
cluded in this series. To date, however, results can be 
reported for the hemispherical nose only. Observa- 
tions of the value of for incipient cavitation were 
made at yaws of 0, 3, and 6 degrees, and these results 
are shown in Figure 10. It is seen that there is a rapid 
increase in Ki with increasing yaw angle. The signifi- 
cance of this is made more apparent by the scale on 
the right of the diagram, which gives the submer- 
gence necessary to avoid cavitation with this hemi- 
spherical nose at a speed of 40 knots. With zero yaw, 
at 40 knots, cavitation will be avoided with a sub- 
mergence of 20 ft, but the submergence will have to 
be increased to 25 ft should the yaw be 3 degrees, and 
with a yaw of 6 degrees, cavitation could not be 
avoided at any submergence less than 37 ft. Of 
course, as the speed is increased or decreased, the 
submergence would have to be increased or decreased 
accordingly. 

Figure 11 shows photographs of the hemispherical 
nose at yaws of 0, 3, and 6 degrees, each for two dif- 


ferent values of K. These pictures show clearly the 
effect of yaw on the shape and position of the cavita- 



Figure 10. Cavitation parameter versus yaw. Hemis- 
pherical nose. 


tion bubble. They also show quite conclusively that 
the plane of the forward edge of the cavitation bubble 



K s 0.35 YAW * 0* K = 0.22 



K « 0.38 


YAW * 6® 


K s 0.23 


Figure 11. Effect of yaw on bubble. Hemispherical nose. 



124 


NOSE CAVITATION — OGIVES AND SPHEROGIVES 





Figure 12. Method of construction. Families of s{)herogives. 


SPHEROGIVE NOSES 


125 





Figure 13. Spherogive profiles arranged as Type 1 families. 




CAL 


126 


NOSE CAVITATION— OGIVES AND SPHEROGIVES 



HALF ANGLE OF SPHERE, 0, DEGREES 

Figure 14. Cavitation parameter, Ki, versus sphere angle. Spherogive noses. 

remains practically at right angles to the direction of 
travel regardless of the yaw, at least for yaw angles 
up to 6 degrees. This is considered one of the inherent 
properties of the spherical nose tip. 

59 SPHEROGIVE NOSES 

Thirty-five spherogive noses of various proportions 
have been tested thus far. The tests on this number 
of noses have furnished interesting and instructive 
data but are not by any means sufficient to predict 
definitely the performance of any given spherogive 
nose. It is believed that enough information is now 
available to permit some general conclusions regard- 
ing the properties of the spherogive family of noses, 
but much yet remains to be done. 

A spherogive nose shape is made by terminating an 
ogive in a segment of a sphere, the curves of the 
sphere and ogive, of course, being tangent at their 
junction. Figure 12 shows that a family of sphero- 
gives can be constructed in three ways: (1) by main- 
taining the radius of the ogive ri constant, which 
gives a series of spheres of varying radii and also 
varying half-sphere angle 6 ; (2) by maintaining the 
half-sphere angle 6 constant, resulting in varying 
values for the radii of both the sphere and ogive; (3) 
by maintaining the radius of the sphere r 2 constant, 
resulting in varying values for the radius of the ogive 
and the half-sphere angle. Some interesting tests of 
families of noses constructed in this manner will be 
discussed. 


The program contemplated tests on five families of 
spherogives based on ogives having radii of 5.0, 3.5, 
2.3, 1.5, and 1.0 calibers. Only a few models were 
made for the 3.5- and 1.5-caliber series and the test 
results on these were not very consistent so emphasis 
will be placed mainly on the 5.0-, 2.3-, and 1.0-caliber 
series. Figure 13 shows profiles of these three families 
of spherogives drawn to scale so their relative shapes 
can be easily observed. Table 2 gives the observed 
values of A for incipient cavitation for the spherogive 
nose shapes tested. 

These values of Ki have been plotted against the 
half-sphere angle 6 for each nose and faired curves 
drawn through the points as shown in Figure 14, 
from which some interesting observations can be 
made. The horizontal portions of the curves represent 
the incipient cavitation parameter for the ogive 
alone, corresponding to those given by the curve in 
Figure 2. This shows that the sphere can be increased 
in size without affecting the incipient cavitation 
parameter until some critical value of the half-sphere 
angle is reached. This region is represented by the 
shaded zone at the break in the curves. This shaded 
region represents a transition from cavitation on the 
ogive to cavitation on the sphere. In other words, all 
nose shapes represented by the curves in the region 
above the shaded zone will cavitate first on the sphere 
and all below this zone will cavitate first on the ogive. 
The line of demarcation is not definite, for, as might 
be expected, cavitation can occur on the ogive and on 
the sphere simultaneously. 


BUBBLE DIMENSIONS FROM PHOTOGRAPHS 


127 


Table 2. Incipient cavitation parameter Ki for 
spherogive noses. 


Ogive radius 
r< 

in calibers 

Half-sphere 
angle 6 
in degrees 

Observed 

Ki 

Ki for 
ogives only 

5.0 

’ 70 

0.22 

0.22 


72 

0.22 



73 

0.26 



74 

0.27 



76 

0.35 



78 

0.44 



81 

0.54 



84 

0.59 



86 

0.63 


3.5 

74 

0.33 

0.26 


77 

0.45 



80 

0.54 


2.3 

69 

0.33 

0.32 


71 

0.35 



72 

0.35 



74 

0.40 



76 

0.45 



78 

0.50 



801^ 

0.58 


1.5 

72 

0.46 

0.37 


74 

0.47 



76 

0.55 



78 

0.54 


1.0 

63 

0.49 

0.43 


65 

0.51 



67 

0.49 



70 

0.52 



72 

0.53 



74 

0 55 



76 

0.60 



78 

0.63 



Figure 14 can be used for the design of spherogive 
noses to fit varying requirements for bluntness and 
incipient cavitation. 

The data given in Figure 14 make possible the 
plotting of another chart showing the relation be- 
tween the radii of the sphere and ogive, the half angle 
of the sphere and the cavitation parameter. This 
chart appears as Figure 15 and covers the whole field 
of possible spherogives, although available data per- 
mit the plotting of only a portion of the curves in- 
volved. As will be seen, this chart gives the radius of 
the sphere corresponding to any half-sphere angle 
and several values of ogive radius. In addition, there 
appear dotted lines of constant K values for incipient 
cavitation. The shaded zone is similar to that in 
Figure 14 in that it represents the region of transition 
from cavitation on the ogive to cavitation on the 
sphere. 

An inspection of Figure 15 shows a surprisingly 
small region in which the cavitation is governed by 


the sphere. It also shows that the longer the ogive 
radius, the larger the half-sphere angle can be with- 
out increasing the incipient cavitation parameter. 
The shaded zone, representing the region of transi- 
tion from cavitation on the ogive to cavitation on the 
sphere, appears to intercept the horizontal axis at 
about an 80-degree half-sphere angle, indicating that 
cavitation will always be on the sphere for angles 
above 80 degrees regardless of the ogive radius. 

5 10 BUBBLE DIMENSIONS 

FROM PHOTOGRAPHS 

® ^ Hemispherical Nose 

The water tunnel is equipped for making photo- 
graphs of a model during the various stages of cavi- 
tation. These can be taken from the side, as in Fig- 
ures 16 and 18, or from the top, as in Figure 17, when 
the effect of yaw is to be shown. As can be seen, these 
photographs give very clear and distinct details of 
the cavitation bubbles so they can be measured for 
the determination of bubble dimensions. A few illus- 
trations of the utilization of the measurements of 
photographs will be given for a model equipped with 
a hemispherical nose. 

In Figure 16 is shown one of a series of photographs 
of the bubble, produced by a hemispherical nose, for 
various values of the cavitation parameter K. These 
photographs were measured to determine the length 
of the bubble from the point of the beginning of cavi- 
tation to the end of the bubble proper (miscellaneous 
small bubbles in the wake of the main bubble are 
neglected). The results of these measurements are 
plotted in Figure 19 as against bubble length in 
calibers. Considering the many inaccuracies involved 
in determining the actual bubble size, it is believed 
the results are satisfactory. This figure shows that 
there is little change in bubble length at the higher 
values of K but the increase is very pronounced as 
the lower values of K are approached. 

The variation in bubble length with yaw is shown 
in Figure 20. In this case the length of the bubble was 
measured on the starboard side and the yaw angle 
was positive, in other words, the nose was deflected to 
the starboard side. The points are not as consistent as 
could be desired but they do show that the bubble 
length increases about 20 per cent when the yaw is 
increased from 0 to 6 degrees. 

Figure 17 is a top view of the model at 6-degree 
yaw and with K = 0.27, and Figure 18 is a side view 


128 


NOSE CAVITATION— OGIVES AND SPHEROGIVES 



Figure 15. Relation between radius of sphere, radius of ogive, half angle of sphere and incipient cavitation parameter 
for ogives and spherogives. 


taken simultaneously. A series of these top and side 
view photographs was measured to determine the 
length of the bubble on the starboard side as well as 



Figure 16. Hemispherical nose; 0 degree yaw. K = 
0.24. Side view. 



Figure 17. Hemispherical nose; 6 degrees yaw. K = 
0.27. Top view. 

the maximum diameter of the bubble and the dis- 
tance from the nose tip to the point at which the 
maximum diameter occurred. The bubble length was 


taken from the side views of which Figure 18 is a 
sample. The maximum bubble diameter and its 
distance E from the nose tip were measured as shown 
in Figure 17. One-half the maximum diameter of the 
bubble was taken as the distance from the centerline 
of the spherical nose to the edge of the bubble. Figure 
21 shows the variation of the distance E with the 
cavitation parameter K, for yaws of 0, 3, and 6 de- 



Figure 18. Hemispherical nose; 6 degrees yaw. K = 
0.27. Side view. 


grees. It is seen that the point of maximum bubble 
diameter recedes rapidly from the nose tip with de- 
creasing values of K. The yaw angle seems to have 
little effect on E, at least for values less than 6 
degrees. 

Figure 22 shows the value of the maximum diam- 
eter of bubble for yaws of 0, 3, and 6 degrees. Here 
again the maximum diameter of bubble increases 
with decreasing K and the yaw angle has little effect. 






BUBBLE DIMENSIONS FROM PHOTOGRAPHS 


129 


Referring to Figure 17, it is seen that when the 
projectile is yawed, the bubble tends to follow the 
direction of the line of travel and in doing so the edge 
of the bubble on the top of the projectile forms a 
definite angle a with the line of travel. Many of these 



Figure 19, Cavitation parameter, K, versus length of 
bubble, (0 degree yaw). Hemispherical nose. 


diameter, in calibers, obtained. In the entire group of 
noses measured the sphere radius varied from a 
minimum of 0.211 calibers to 0.500 calibers, the 
maximum for the hemisphere. 

050 


040 


UJ 

5 030 


i 

^020 

> 


010 


0 

Figure 21. Cavitation parameter, K, versus nose tip to 
maximum diameter of bubble. Hemispherical nose. 



12 3 4 5 

DISTANCE, NOSE TIP TO MAX OIA OF BUBBLE, CALIBERS 


angles were measured for various values of K and 
yaw and the results are plotted in Figure 23. No 
attempt has been made to investigate this phenome- 
non further or to determine its significance. 



LENGTH OF BUBBLE, CALIBERS 


Figure 20. Cavitation parameter, K, versus length of 
bubble, (0, 3, and 6 degrees yaw). Hemispherical nose, 

® ^ Spherogive Noses 

An attempt was made to determine the effect of 
the radius of the sphere on the maximum diameter 
of the full cavitation bubble. Photographs of the 
1.0-, 2.3-, and 5.0-caliber spherogive noses under full 
cavitation were carefully measured and the bubble 


In Figure 24 the maximum bubble diameter has 
been plotted against the radius of the sphere, both in 
calibers. It is remarkable to note that there appears 
to be a linear relationship between these two quanti- 
ties, although it must be remembered that the meas- 



Figure 22. Cavitation parameter, K, versus maxi- 
mum diameter of bubble. Hemispherical nose. 


urement of these small photographs is subject to 
many errors. 

The 5.0-caliber series is the only one in which it 
was possible to make measurements of the bubble 
diameter for values of the sphere radius in the region 


130 


NOSE CAVITATION— OGIVES AND SPHEROGIVES 


where cavitation occurred on the ogive only. There 
are two noses with sphere radii of 0.211 and 0.268 
calibers which have the same bubble diameter. This 
is not unexpected as this is the bubble diameter for 
the ogive, the sphere having no effect. The dotted 
horizontal lines indicating the bubble diameters for 
2.3- and 1.0-caliber ogives are assumptions, although 
they are believed to be fairly accurate as they are 
drawn to correspond approximately to the bubble 
diameters for noses close to the transition point. No 
photographs have been taken of the full bubble pro- 
duced by ogive noses, so the diameters of these could 
not be determined by measurement. 



0 10 20 30 40 50 60 70 

ANGLE, oC . DB3REES 


Figure 23. Cavitation parameter, K, versus angle a, 

of bubble with flow. Hemispherical nose. 

Figure 24 furnishes good evidence to support the 
theory that the full bubble diameter is determined by 
the sphere radius. (See Chapter 4.) 

5 “ EFFECT OF THE SPHERE SIZE 

It has been shown that the full bubble diameter is 
determined by the radius of the sphere. The curves in 
Figure 14 show that incipient cavitation is governed 
by the half angle of the sphere B for a given ogive. It 
is also true that the half angle of the sphere deter- 
mines the extent and nature of the cavitation bubble 
during its development after the point of incipient 
cavitation has been passed. In Figure 25 have been 
assembled photographs of cavitation effects on spher- 
ogive noses having ogive radii of 1.0, 2.3, and 5.0 
calibers and half-sphere angles of 72 and 76 degrees. 

Comparing photographs A and F of Figure 25, of 
the 1.0-caliber series for a A of 0.21, it is seen that in- 
creasing the half-sphere angle 6 from 72 to 76 degrees 
greatly increases the size of the cavitation bubble. 


The 72-degree sphere produces a bubble only slightly 
longer than the projectile, whereas the 76-degree 
sphere produces practically a full cavitation bubble. 
A comparison of B and G for a higher value of K 
shows a decided increase in the extent of the bubble 
for the larger sphere angle. A like comparison can be 
made with the photographs of the 2.3-caliber and 
5.0-caliber series; in every case there is a pronounced 



RADIUS OF SPHERE, , CALIBERS 


Figure 24. Radius of sphere versus diameter of fully 
developed bubble on spherogive noses at zero yaw. 

increase in the cavitation effect due to increasing the 
half-sphere angle with the cavitation parameter 
remaining constant. 

In connection with Figure 25, it is interesting to 
note that photographs B, H, I, and J show cavitation 
on both the sphere and the ogive. 

Figure 26 shows how the cavitation bubble is 
affected by variations in the ogive and sphere radii, 
the half-sphere angle remaining constant. Photo- 
graphs A, B, C, and D show the bubble for four 
spherogive noses with a half-sphere angle of 72 de- 


COMPARISON OF OGIVE AND SPHEROGIVE BUBBLES 


131 


grees and K remaining constant at 0.21. It is seen 
that there is an increase in the size of the cavitation 
bubble as the nose becomes more and more blunt. 
The four pictures on the right, E, F, G, and H were 
selected to show approximately the same degree of 
cavitation, and it should be observed that the value 
of K, for this condition, increases as the bluntness of 
the nose increases. 

The effect of varying the half-sphere angle is 
shown in Figure 26 of Chapter 4, which is a series of 
photographs of a family of 5.0-caliber spherogives. In 
this case the 74-degree sphere appears to be at the 
transition point as cavitation is occurring on both the 
ogive and the sphere. The noses with spherical angles 
less than 74 degrees cavitate on the ogive and for 
angles of greater than 74 degrees the cavitation is on 
the sphere only. The last five photographs have been 
selected to show approximate!}^ the same degree of 


cavitation and it is seen that as the noses increase in 
bluntness, i.e., from 76 to 86 degrees for the half- 
sphere angle, the value of K increases from 0.25 to 
0.57. Stating this in terms of submergence and speed, 
the 76- and 86-degree noses would have the same 
degree of cavitation at a speed of 60 knots with a 
submergence of 57 ft for the 86-degree nose and only 
7 ft for the 76-degree nose. 

5 12 COMPARISON OF OGIVE 

AND SPHEROGIVE BUBBLES 

Comparisons have already been made between the 
cavitation parameters for ogives and spherogive 
noses at the point of incipient cavitation. It would be 
instructive to observe the development of the cavita- 
tion bubble on the two types of nose for values of K 
lower than that for incipient cavitation. 




e * 7z 


1.0 CAL SPHEROGIVE * 


e* 76® 




K = 0.2I 




K=0,29 


e« 72' 


2.3 CAL SPHEROGIVE 


e « 0.76® 


A 

K*0.2I 


B 

K=0.28 


F 

K = 0.2I 


G 

K:0.29 


J 

K=0,I9 


5.0 CAL. SPHEROGIVE 


e « 76® 


Figure 25. Effect of size of sphere on cavitation parameter. Spherogive noses. 




132 


NOSE CAVITATION— OGIVES AND SPHEROGIVES 



Figure 26. Cavitation bubbles; 72-degree spherogives. 


The first series of photographs in Figure 27A.to C, 
shows the cavitation bubbles at a A of approximately 

0.25 for the following nose shapes: 1.0-caliber ogive, 
and 1 .0-caliber by 6.5-degree, 2.3-caliber by 76-degree, 
3.5-caliber by 77-degree, and 5.0-caliber by 78-degree 
spherogives. All these shapes, excepting the 1.0-cali- 
ber by 65-degree spherogive, have approximately the 
same K for incipient cavitation (0.43 to 0.45). The 
1.0-caliber by 65-degree spherogive has a somewhat 
higher A,, and it has been included as it was the best 
available photograph showing a spherogive cavitat- 
ing on the ogive only. It will be seen that the bubbles 
for the three spherogives C, D, and E are of about the 
same size, and that cavitation is taking place on both 
the sphere and the ogive. The 1.0-caliber by 65-degree 
spherogive (B) is cavitating on the ogive only as the 
spherical segment is so small that it has no effect. It 
is of interest to note that the bubbles in photographs 
A and B are of the same size, which should be the case 
as both are for 1.0-caliber ogives at a A of 0.26. 

The second series of photographs in Figure 27 (F 
to I), shows the cavitation bubbles at a K of approxi- 


mately 0.19 for the following noses: 1.5-caliber ogive, 
and 2.3-caliber by 72-degree, 3.5-caliber by 74-de- 
gree, and 5.0-caliber by 76-degree spherogives. All of 
these noses have nearly the same Ki (0.34 to 0.37). In 
this series also it is observed that the bubbles for the 
spherogives are of practically the same size, while 
that on the ogive is. of much smaller size. 

From these preliminary data it seems reasonable to 
draw four conclusions subject to revision after more 
complete test results are available: 

1. Spherogive noses with spherical segments larger 
than the critical angle and having the same Ki will 
have practically the same size and type of bubble at 
lower values of K. 

2. If an ogive and a spherogive with a spherical 
segment larger than the critical angle have the same 
Ki, the bubble formed at lower values of K will be 
shorter for the ogive than for the spherogive. 

3. If an ogive and a spherogive have the same 
radius for the ogive, the values of Ki and the size of the 
cavitation bubbles will be the same for both noses if 
the spherical segment is smaller than the critical angle. 




CONCLUSIONS 


133 


4. The cavitation bubble originating on a spherical 
tip develops faster as K is reduced than one starting 
at the same Ki which originates on a surface of 
larger radius of curvature such as an ogive. 

5 13 MEASUREMENTS OF PHOTOGRAPHS 

All models have been made 2.00 in. in diameter so 
this can be used as the unit of length for measure- 
ments made on photographs. Owing to the unequal 
horizontal and vertical distortion caused by the Lu- 
cite window in the tunnel, the diameter of the model 
will represent 2 in. in the vertical direction and 1.83 
in. in the horizontal direction. 

31* CONCLUSIONS 

Although based on incomplete data, the following 
conclusions seem to be justified: 

1. The incipient cavitation parameter Ki for ogive 
noses drops rapidly as the ogive radius is increased 
from 0.5 to 1.0 caliber, the decrease being much less 
pronounced for radii between 1.0 and 8.0 calibers. 

2. The ogive radius drawn to this forward edge of 
a well-developed cavitation bubble makes an angle 
of about 86 degrees with the axis of the nose. This 
angle seems to be constant for all noses investigated. 

3. The incipient cavitation parameter Ki increases 
rapidly with an increase in yaw angle. For a hemi- 
spherical nose Ki increases from 0.75 for zero yaw to 


1.01 for 6 degrees yaw. 

4. Photographs of well-developed bubbles on a 
hemispherical nose indicate that the plane of the for- 
ward edge of the bubble remains practically at right 
angles to the direction of travel for yaw angles up to 
at least 6 degrees. 

5. When the sphere segment on spherogive noses 
is large compared to the ogive, cavitation occurs first 
on the sphere so that the inception and subsequent 
growth of the cavitation bubble depend only on the 
sphere size. When the sphere segment is small com- 
pared to the ogive, cavitation occurs first on the 
ogive, and the inception and subsequent bubble 
growth depend on the ogive and are independent of 
the sphere size. The critical sphere size dividing the 
two behaviors is different for different spherogive 
families. For the 5.0-caliber family of spherogives, 
this critical sphere size corresponds to a half-sphere 
angle d of about 72 degrees, and for the 1.0-caliber 
family, this angle is about 60 degrees. 

6. Based on measurements of photographs, it ap- 
pears that the maximum diameter of the full cavita- 
tion bubble on spherogive noses varies directly with 
the radius of the sphere regardless of the ogive radius. 

7. For a given family of spherogives, based on a 
constant ogive radius, the value of K for incipient 
cavitation, Ki, will be determined by the half-sphere 
angle. The blunter the nose, the higher the value. 


A 

1.0 CALIBER 
OGIVE 
KjsO.4 3 
K=0.26 


B 

1.0 CALX 65® 
SPHEROGIVE 
Kp 0,51 
K* 0.26 


C 

2.3 CAL X76® 
SPHEROGIVE 
K--0.45 
K =0.25 


D 

3.5 CALX77® 
SPHEROGIVE 
Kj = 0.43 
K = 0.24 


E 

5.0 CAL X78® 
SPHEROGIVE 
Kj=0.4 3 
K = 0.24 



NOTE -THE LIHfS ON THE PHOTOGRAPHS 
ARE 1 CALIBER APART 


F 

1.5 CALIBER 
OGIVE 
K; = 0.37 
X =0.19 


G 

2.3 CAL X72® 
SPHEROGIVE 
Ki»0.36 
K=0.I9 


H 

3.5 CAL X74® 
SPHEROGIVE 
Ki=0.34 
K = 0.I8 


I 

5.0 CALX 76° 
SPHEROGIVE 
Ki=0.35 
K=0.I9 


Figure 27. Comparison of ogive and spherogive bubbles. 


Chapter 6 

HYDRODYNAMIC FORCES RESULTING FROM CAVITATION ON 

UNDERWATER BODIES 


PURPOSE AND SCOPE 
OF INVESTIGATION 

iTH THE INCEPTION and growth of cavitation, the 
distribution of velocities and pressures around a 
moving body are changed, and the hydrodynamic 
forces are different from those existing under cavita- 
tion-free conditions. In the case of underwater pro- 
jectiles, most interest is in the two extreme condi- 
tions — the initial stages immediately after the onset 
of cavitation and the fully developed stage when a 
large portion of the cavitating body is enclosed in a 
vapor cavity. For the initial stages, it is important to 
know how far cavitation can develop before affecting 
the forces and moments appreciably, as well as the 
magnitude of the resulting forces. This phase applies 
to the steady underwater run of all high-velocity tor- 
pedoes. For the fully developed condition, a knowl- 
edge of the forces and moments and the physical con- 
ditions of flow affecting these forces are important. 
This phase also applies to the air-water entry prob- 
lems arising for various projectiles where the air 
cavity which is obtained at entry is similar, if not 
identical, to the vapor cavity which is obtained 
with cavitation. 

In order to investigate these different aspects, 
measurements of forces and moments were made for a 
variety of bodies subjected to cavitating conditions 
in the high-speed water tunnel. Complete projectiles 
with different noses and tail structures were tested to 
determine; the total performance for the incipient and 
more developed stages of cavitation. Short bullet- 
shaped models with different noses were tested to 
obtain the effect of the nose shape alone, primarily 
for fully developed cavitation. 

In addition to the measurements on three-dimen- 
sional bodies, that is, bodies of revolution, tests were 
made for cavitating and noncavitating flow of the 
drag of a cylinder with its axis normal to the direction 
of motion. The drag of this two-dimensional case and 
of two of the three-dimensional shapes are compared 
with values calculated from measured pressure dis- 
tributions on the body surface. 


6 2 the effect of cavitation 

ON DRAG 

6.2.1 Physical Growth Necessary 
to Change the Drag 

The amount of cavitation necessary to cause a 
measurable change in drag is dependent somewhat on 
the shape of the body, the kind of cavitation that is 
formed, and the relative magnitude of the drag with- 
out cavitation. The results of measurements on 
several different bodies, and photographs of the cavi- 
tation at various stages of development are shown in 
Figures 1 to 11. The pictures were obtained with ex- 
posures of the order of 20 ^sec so that the flow was 
effectively “stopped.” The drag measurements are 
presented as curves of the drag coefficient Cd plotted 
against the cavitation parameter K. Decreasing val- 
ues of K represent conditions for increased cavita- 
tion. The methods of evaluating and correcting the 
test data and a list of symbols and definitions are 
given in the Appendix. 

Hemisphere Nose 

The first two sets of data were obtained with a 
cylindrical body having an ogival tail or afterbody 
with a hemisphere nose in one case, and with a 
square-end nose in the second. With this simple form 
a good comparison of the effect of nose shape should 
be obtained. Flash photographs of cavitation on the 
hemisphere are shown in Figure 1 . The outline of the 
projectile can be seen in the first photograph, while in 
the second photograph, a small band of fine-grained 
cavitation is seen just aft of the junction between the 
hemisphere and the cylinder. In the bottom two 
photographs, the entire body is enveloped in a cavi- 
tation cavity. The drag coefficient of this body is 
shown in Figure 2 as a function of the cavitation pa- 
rameter K. On this figure the dashed curve represents 
Cd values calculated from measured pressure distri- 
butions and will be discussed in detail later. The 
curve of measured Cd values shows that there is no 
sudden increase in drag with the onset of cavitation. 



134 


THE EFFECT OF CAVITATION ON DRAG 


135 


Instead, with increasing cavitation (decreasing K) 
the resistance increases very slowly until a K of about 
0.5 is reached, when the cavitation zone on the nose 
is about Y 2 caliber long, as can be visualized by inter- 
polation between photographs. With further develop- 
ment of cavitation, however, Cd rises rapidly to 



K 


K 


K 


K 


Figure 1. Cavitation on cylinder with hemispherical 
nose and ogival tail. Yaw = 0 degree. 

several times its initial value. A peak value is reached 
after which C d tends to decrease as the trend of the 
calculated dashed curve would predict. 


develops, but increases very slowly until the wispy 
formation coalesces to form the white plume. This 
increase is at about the same rate as observed for the 
hemisphere, but is a much smaller percentage of the 
total drag. Here, in order to increase the drag ma- 
terially above its already high value, it is necessary 
that enough cavitation be formed to displace the flow 
away from the body further than for noncavitating 
flow separation and to increase the turbulent wake 
downstream. 


Various Noses on a Torpedo 


Measurements for a ring-tailed torpedo with ex- 
haust stacks in the ring are shown in Figure 5. No 
photographs were obtained with the test, but the 
development of cavitation at various points on the 


0.6 


- 0.4 

H 

Z 

Ui 

0 

1 

8 0.2 
5? 

s 




1 

CAVITATI 

DOMPLE 

BODY 


— 5 

§ 

1 

1 — 

ft 

\ 

- — 1 

1 

-T Hi- 



CALC 
PRES 
_ DUF 
C4 

FROM 
S DIST 
tING 

1 1 


-I* 

c 

las 

goz 

w 





IT Z ^ 

\ Si 

i 

m 

> 

- OC. 



y 



\5-> 

\l 

< 

0 

1 

cz 

1 
























02 


0.4 06 0.8 

CAVITATION PARAMETER, K 


Figure 2. Effect of cavitation on drag of cylinder 
with hemispherical nose and ogival tail. Yaw = 0 
degree. 


Square-End Cylinder 

In Figures 3 and 4, data are shown for the cylinder 
with the square end. This ‘^nose” produces the wispy 
type of cavitation at inception which develops into a 
fine-grained white plume and ultimately to a clear- 
walled cavity extending back from the separation 
point in the sharp edge as cavitation increases. 

The drag without cavitation is initially nearly ten 
times the value for the hemisphere. It is almost com- 
pletely form drag caused by separation of the non- 
cavitating flow from the body at the sharp corner of 
the nose. As in the case of the hemisphere, the drag 
does not change suddenly as cavitation forms and 


projectile is described by notes on the curves. Two 
noses were used with this projectile. One, the so- 
called Mark 13 nose, is composed of a 23/^-degree in- 
cluded angle cone, tapering down from full diameter 
to 0.92 degree of the maximum diameter, with a spher- 
ical segment tip having an 883^-degree half angle. 
The other, a 2.3-caliber by 78-degree spherogive, is 
formed by replacing the pointed tip of a 2.3-caliber 
ogive with a spherical segment which becomes tan- 
gent to the ogive surface at a half angle of 78 degrees. 

The Mark 13 nose is very little different from a 
hemisphere and produces the same type of cavitation 
just aft of the tangent point with the conical surface. 
Inception is obtained at a K of about 0.66 instead of 



136 


FORCES RESULTING FROM CAVITATION 


0.75, however. The tail structure and the nose begin 
to cavitate at about the same time. There is no 
measureable change in drag on this projectile immed- 
iatel}^ after the onset of cavitation. Cd increases ma- 
terially only after a moderate band is developed on 
the nose (less than for the hemisphere on the cylin- 
drical body, however) and pronounced cavitation 
develops on parts of the tail structure. 

The spherogive nose has much better character- 
istics than either the hemisphere or the Mark 13 and, 
consequent!}^, does not cavitate until K is reduced to 



Figure 3. Cavitation on square-end cylinder with 
ogival tail. Yaw = 0 degree. 


approximately 0.5. As a result, tail cavitation is well 
developed before nose cavitation appears and causes 
the drag to increase while the nose cavitation is still 
in.its early stages. 

Blunt Nose on a Depth Bomu 

A depth bomb with a ring tail and a blunt nose was 
tested and the results are shown in Figures 6 and 7. 
The nose is a 1 -caliber ogive truncated so the di- 
ameter of the face is % caliber. The edge of the flat 
face is rounded slightly. The initial cavitation on this 
projectile forms on the ogival surface at the junction 


with the flat face and is very fine-grained in character. 
The tail surfaces begin to cavitate soon after incep- 
tion on the nose. The cavitation-free drag of the pro- 
jectile is about three times the value of the drag of 
the simple body with hemisphere nose shown in Fig- 
ure 2. With the onset of cavitation, there is, if an}^- 
thing, a slight tendency for the drag to drop off. An 
increase is obtained, however, with a relatively small 
amount of cavitation on the nose and the tail. In 
fact, the rapid increase in drag of this particular pro- 
jectile occurs with less visible cavitation than on any 
of the other models discussed thus far. 



Figure 4. Effect of cavitation on drag on square-end 

cylinder with ogival tail. Yaw = 0 degree. 

Effect of Yaw 

A set of data showing the effect of cavitation with 
yaw is shown in Figure 8 for the Mark 13-2 torpedo 
with a hemisphere nose, the Mark 13 nose, and a 5- 
caliber by 7()-degree spherogive nose. Photographs of 
the cavitation are shown for each nose in Figures 9, 
1 0, and 1 1 . The curves of Figure 8 show results similar 
to those already observed at zero yaw. With the hem- 
isphere and Mark 13 nose very little change in drag 
occurs until cavitation is fairly well developed on 
both the nose and the tail surface. Actually cavitation 
appears first on the tail ring at about K = 0.9 and 
later on the lee side of the hemisphere at K = 0.83. 
The drag with the hemisphere nose is only 10 per 
cent greater at K = 0.62 when the cavitation band 
on the nose has grown to a length of about 3^ caliber. 
With the Mark 13 nose, nose cavitation appears at 
lower K as does the sharp increase in drag. Here the 
influence of the tail caA’itation becomes more im- 


THE EFFECT OF CAVITATION ON DRAG 


137 


portant. With the 5-caliber by 76-degree spherogive, 
nose cavitation does not appear at all until after 
cavitation on the tail and, in this case, on the after- 
body also, has caused the drag to rise. The principal 
effect of the yaw seems to be that all stages of cavita- 
tion occur earlier, that is at higher values of K than 



Figure 5. Effect of cavitation on drag of ring tail 
torpedo with 4 exhaust stacks. Yaw = 0 degree. 


amount of cavitation formed at this point occupies an 
appreciable physical volume. 


6.2.3 Effect on Boundary Layer and 
Skin Friction 

In general, the drag of bodies is the sum of skin 
friction and form drag. As cavitation develops, the 
relative proportions of the two components are 
changed. Finally for fully developed cavitation where 



do the corresponding stages on the body with zero 
yaw. The result is that for any constant value of K 
less than Ki, the drag increases more rapidly with 
yaw than it does for the noncavitating condition. 

® ^ ^ Summary 

To summarize, these examples show the common 
effects that the onset of cavitation as observed visu- 
ally does not result in an immediate sharp increase in 
drag. Instead, the drag increases slowly, and in one 
case actually tends to drop off slightly, until sufficient 
cavitation is formed to change the basic flow pattern 
around the object. For all cases except one, the 


Figure 6. Cavitation on blunt-nosed depth bomb (1- 
caliber ogive truncated to ^-caliber flat face with edge 
rounded). Yaw = 0 degree. 

the projectile is completely enclosed in a cavity, and 
contacts the fluid only over a small area at the nose 
tip, the drag becomes almost 100 per cent form drag. 
The kind of effect cavitation produces will depend on 
the body shape which determines the ratio of form 
drag to skin friction for noncavitating conditions. 
The influence of cavitation in affecting the form drag 
can be visualized rather clearly, since the effective 
shape of a body is, of course, changed by the bubble 
formation. The physical mechanism of its effect on 
skin friction can be explained qualitatively by com- 





138 


FORCES RESULTING FROM CAVITATION 


parison with local separation and its effects on the 
boundary layer development.^ ®’^’* 

For cases where the drag is due primarily to skin 
friction, it will be highest when the boundary layer is 
turbulent. At a given Reynolds number (based on the 



Figure 7. Effect of cavitation on drag of blunt-nosed 
depth bomb (1 -caliber ogive truncated to 3^-caliber flat 
face with edge rounded). Yaw = 0 degree. 

length of the projectile in direction of motion), if an 
appreciable portion of the boundary layer is laminar, 
Cd will be much lower. Any influence which causes an 
early transition to a turbulent layer will tend to 



Figure 8. Effect of cavitation on drag of Mk 13-2 
torpedo with three different noses. Yaw = 3 degrees. 


increase Cd- In noncavitating flow, this can be 
accomplished by increasing Reynolds number and/or 
increasing the turbulence in the surrounding fluid. It 
can also be accomplished artificially by providing 
roughness or obstructions on the surface of the body. 


or discontinuities in the curvature at the surface that 
will cause local separation of the flow, and hence in- 
troduce turbulence. 

For the types of cavitation already discussed, a 
definite similarity exists between the cavitation and 
separation. Reference to Figure 1 shows that fine- 
grained cavitation forms a ring just aft of the junc- 
tion between the hemisphere tip and the cylinder. 
Figure 3 shows thin wisps forming in eddies well 



K =0.71 





K =0.62 





0.49 


Figure 9. Hemisphere nose on Mk 13-2 torpedo. 
Yaw = 3 degrees. Top and side views. 

away from the projectile surface. Figure 6 shows fine- 
grained cavitation appearing at the discontinuity be- 
tween the flat-face and the ogive surface of the nose. 
Each of these has the common characteristic that 
cavitation appears first at or near a discontinuity in 
surface curvature. 

In Figure 12, in the left column, are flow line dia- 
grams for these same noses on which the zone of 
separation is shown. These diagrams were drawn from 
actual observations in the polarized light flume*’® at 





THE EFFECT OF CAVITATION ON DRAG 


139 


very low Reynolds numbers, so the separation effects 
are exaggerated. However, it is clear that for these 
cases, both separation and cavitation occur in the 
same general vicinity. In the initial stages, therefore, 
cavitation must be similar to separation in its effect 
on the drag. This idea is in agreement with the cases 
discussed thus far. 



K = 0.40 


Figure 10. Standard Mk 13 nose on Mk 13-2 torpedo. 

Yaw = 3 degrees. Top and side views. 

With the blunt-nosed bodies, the form drag is 
initially high due to severe separation. Incipient cavi- 
tation occurs in the same zone as the separation and 
has practically no effect on the drag. With bodies 
having sharp discontinuities in surface curvature such 
as that between the hemisphere and the cylinder, the 
boundary layer probably starts as predominantly 
turbulent, so that cavitation alters the conditions 
only slightly. Cd increases materially only with the 
development of enough cavitation to establish a new 
effective shape for the body, and hence alter both 
skin friction and form drag. 


With more streamlined noses, separation does not 
occur under normal conditions and the boundary 
layer remains laminar over a longer distance from the 
tip of the nose. The minimum pressure on the body 
surface usually occurs at some point ahead of the 
maximum diameter so that it is possible that, on 
small projectiles at least, cavitation occurs in the 
normally laminar zone. The bottom diagram in Fig- 
ure 12 for the semiellipse illustrates this possibility. 



K* 0.31 


Figure 1 1 . Five-caliber by 76-degree spherogive nose on 
Mk 13-2 torpedo. Yaw = 3 degrees. Top and side views. 

Cavitation under these conditions should result in a 
transition to a turbulent boundary layer with a 
change in drag. For large projectiles the boundary 
layers for most velocities are almost completely tur- 
bulent so that this condition is of secondary im- 
portance. Also, with increased body fineness, the 
type of cavitation changes to coarse-grained so that, 
while turbulence is introduced, it is somewhat dif- 
ferent from that formed by local separation and the 
analogy may not hold so closely. 


140 


FORCES RESULTING FROM CAVITATION 


As cavitation grows, it effectively changes the shape 
of the body and thereby alters the form drag. Simul- 
taneously, the skin friction should decrease because 
there is less high-velocity fluid in contact with the 
surface. Ultimately, if the cavitation envelops the 
body completely, there remains only form drag due 
to the difference between the pressure forces on the 









Figure 12. Flow line diagrams and cavity silhouettes. 


small wetted area of the nose and the gas pressure 
in the bubble. The pressure distribution along the 
surface of the solid body is altered completely, while 
the effective body is enlarged by the extent of the 
cavitation bubble. The right-hand diagrams in Fig- 
ure 12 show the full cavity conditions for the noses 
already discussed. These were obtained by scaling 
the cavity silhouettes from photographs. 

The drag coefficient curve shown in Figure 7 for a 


depth bomb with a truncated ogive nose indicates a 
slight decrease in Cd with initial growth of cavitation. 
Knapp has suggested^® that with growth of cavitation 
in the early stages after inception the interplay be- 
tween the increase in form drag and possible decrease 
in skin friction might result initially in such a de- 
crease. A similar phenomenon has been measured in 
the case of some centrifugal pumps where measurable 
increases in head and efficiency have been observed 
when the pump impeller began to cavitate."-^^ 


Drag in the Cavity 


With a completely enveloping bubble such that 
contact with the water is made only over a small area 
at the forward portion of the body, skin friction can 
be neglected and all of the drag can be assumed to be 
form drag. This assumption will certainly hold for 
Reynolds numbers (based on diameter) greater than 
on spheres, cylinders, and blunter bodies. For 
more streamlined shapes skin friction will cause a 
small correction. With enveloping bubbles the magni- 
tude of Cd is not a single value but depends on the 
stage of bubble development. The total pressure 
(static plus dynamic) acting over the wetted portion 
of the body will depend on the velocity and on the 
static pressure in the undisturbed fluid while the 
“back pressure” acting over the after portion of the 
body will be independent of the velocity or pressure 
in the undisturbed fluid. This back pressure will be 
constant and equal to the vapor pressure for pure 
cavitation. An expression for Cd in the cavity stage 
showing its variation with bubble growth (and hence 
K) can be obtained by neglecting the skin friction 
and integrating the normal forces acting over the 
entire body surface as follows. 

Writing the pressure or form drag as a summation 
of all components of the pressure forces taken paral- 
lel to the direction of motion gives 

D = P cos dda (1) 


where D 
P 


da 

d 


the pressure force acting in the direction 
of motion, 

the unit normal pressure at any point on 
the body, also 

the static pressure in the undisturbed 
flow plus the pressure resulting from 
dynamic effects, 

an element of area on the body surface, 
the angle between an area element da 
and the direction of motion. 


THE EFFECT OF CAVITATION ON DRAG 


141 


This expression must be integrated over the wetted 
area of the body and the area enclosed by the bubble 
so that 

D = j P cos dda J ^ 

wetted area enveloped area 


Simplifying the expression by writing cos dda = dA , 
an element of area projected on to a plane normal to 
the direction of motion, gives 


D = 


j PdA + 

wetted area 


Z™-*- 

enveloped area 


(2) 


In this normal projection, the net projected area of 
the wetted surface and the bubble-enclosed surface 
are equal and can be denoted by A^. Assuming now 
that P = Pb = constant inside the bubble and 
adding and subtracting Pq, the static pressure un- 
disturbed flow, from the total pressure P, one obtains 
after simplifying, 

D = f(P - Po)dA + (Po - Pb)A^. (2a) 


Dividing by (pv^A)/2 gives the drag coefficient 


- -'D- = -L f 

" “ A Ja. 




P - P 




"dA + (3) 


where A = the area of the maximum section of the 
body projected normal to the direction 
of motion, 

K = (Po - PB)l{pvy2). 

The first term in equation (2) is the integral of the 
pressure intensity caused by dynamic effects. The 
second is merely the difference between the hydro- 
static pressure in the undisturbed fluid and the bub- 
ble pressure. When converted into a coefficient as in 
equation (3) the first term becomes a function of the 
dimensionless dynamic pressure distribution and the 
second a function of the cavitation parameter K. 
When K = 0 the limiting Cd equals the first term of 
equation (3). As the cavity decreases from the full 
bubble stage with increasing K, Cd will increase pri- 
marily because of the increase in Po — Pb- Usually 
the variation in wetted area and pressure distribution 
on the body will have a secondary effect.This trend per- 
sists until the cavity no longer envelops the body and 
hydrodynamic forces begin to act on the after portion 
as well as the nose or leading edge. Depending on the 


body shape and attitude with respect to the flow, the 
drag may increase somewhat farther. Finally, how- 
ever, as the bubble becomes smaller and smaller, Cd 
must approach the normal cavitation-free value. For 
streamlined objects, like most projectiles, this will be 
less than for the cavity stage. For nonstreamlined ob- 
jects, like a cylinder normal to the flow, the cavita- 
tion-free drag may exceed the cavity drag. 

Actual numerical evaluation of Cd from equation 
(3) requires that the pressure distribution denoted 
by the function P be known. An evaluation based 
on actual measurements of the pressures on the sur- 
faces of cavitating bodies will be discussed in a later 
paragraph. 


6 2.5 Effect of Body Shape on Cavity Drag 

To investigate the effect of body shape on drag in 
the cavity, a series of measurements was made using 
models short enough to insure that the entire body 
could be completely enveloped by the cavitation 
pocket at the lowest value of K obtainable in the 
water tunnel. Six different noses were tested on short 
cylinders with either a blunt afterbody or with an 
ogival afterbody. The three basic types of nose shapes 
tested were : 

1. Noses tipped with spherical segments, including 
the hemisphere, the Mark 13, the 2.3-caliber by 78- 
degree spherogive, and the 5-caliber by 76-degree 
spher ogive. 

2. Blunt noses, including the square-end cylinder 
and the truncated ogive. 

3. ‘‘Streamlined” noses typified by a 234-to-l 
semiellipsoid. 


Description of Cavities 

Typical top and side view pictures of the cavities 
formed by these shapes are shown in Figures 13 and 
14. These photographs are not all for the same value 
of K nor for the same degree of bubble development. 
However, the essential features of the influence of 
nose shape can be seen, since further reductions in K 
do not change appreciably the forward portion of the 
cavity. In Figure 13 it will be noticed that for these 
models the cavity separates on the spherical tip so 
that the water is in contact with only a portion of the 
tip. For the blunt noses shown in Figure 14 the cavity 
separates from the body at the sharp edge so that 
water is in contact with only the flat face of the body. 
For the semiellipsoid, also shown in Figure 14, the 




142 


FORCES RESULTING FROM CAVITATION 




HEMISPHERE 
K =0.29 


2.3 CAL X 78*" 
SPHEROGIVE 
K = 0.27 




5 CAL X 76' 
SPHEROGIVE 
K = 0.21 


Figure 13. Cavitation bubbles on spherical-tipped noses. Yaw = 0 degree. 




THE EFFECT OF CAVITATION ON DRAG 


143 


cavitation is of the coarse-grained type and clean 
separation is not obtained even though most of the 
body is enveloped so that only the nose proper is in 
contact with the water. The pictures also show the 
expected result that the cavity diameter increases 
Avith bluntness of the nose. Thus the square-end cyl- 
inder produces the largest cavity, and the 5-caliber by 
76-degree spherogive or the 23/^-to-l semiellipsoid, 


the smallest. It is interesting to note that the trun- 
cated ogive produces a bubble which at a given dis- 
tance from the separation point has about the same 
diameter as that produced by the hemisphere nose in 
spite of its bluntness. This is no larger because the 
diameter of the face is only % caliber and because, 
further, the edge of the flat face is rounded off to a 
small radius. 


SQUARE END 
CYLINDER 
K=0.39 


TRUNCATED OGIVE 
K= 0.29 


2-1/2:1 ELLIPSOID 
K =0.24 



Figure 14. Cavitation bubbles on flat-faced and ellipsoidal noses. Yaw =0 degree. 


144 


FORCES RESULTING FROM CAVITATION 


Drag versus K 

The measured values of Cd for these shapes are 
shown in Figure 15 plotted against the cavitation 
parameter K. Interest is centered mainly on the 
\ow-K end of each curve which is shown by a heavier 
line to indicate that the body is completely enveloped 
in the cavitation l^ubble. On this same diagram are 
plotted the same calculated values for the square-end 



NOTE: BODY COMPLETELY ENVEUDPED BY CAVITATION BUBBLE 
IN ZONE MARKED BY HEAVY CURVE. 

Figure 15. Effect of nose shape on drag in the cavity. 

Yaw = 0 degree. 

cylinder and the hemisphere as were shown in Fig- 
ures 2 and 4. These were calculated using equation 
(3) above, and the measured pressure distributions 
on the surface of these noses. The calculated co- 
efficients are extrapolated from the points indicated 
by crosses down to zero K. 

For a given value of K the measured magnitudes of 
Cd reflect the difference in bubble size already ob- 
served, the square-end cylinder showing the largest 
and the 5-caliber by 76-degree spherogive and the 
23^to-l ellipsoid the smallest. This is a necessary 
relationship since the cavity diameter is a measure of 
the momentum change imparted to the water as the 


nose pushes it aside and hence is proportional to the 
drag. Thus Cd also is measured by the cavity di- 
ameter relative to the projectile diameter. This de- 
pendence of Cd on the bubble diameter does not hold, 
however, if one compares cavity sizes produced by 
the same projectile at different values of K. As K is 
reduced, it is easier for a body to make a cavity be- 
cause the momentum required is reduced in propor- 
tion to the pressure forces, represented by Po — Pb, 
Avhich must be overcome. Consequently, C d becomes 
smaller with reductions in K even though the bubble 
grows larger. 

The truncated ogive has a lower drag than would 
be calculated normally for the equivalent-sized 
square-end cylinder because of the slight rounding of 
the corner. Its drag coefficient is calculated to be 
about 50 per cent greater with a sharp edge. In all 
cases, as equation (3) states, a reduction in drag co- 
efficient with reduction in K is discerned soon after 
the body is completely enveloped. The measurements 
for the hemisphere and the square-end cylinder with 
the enveloping cavity are both slightly lower than 
the calculated values. It is interesting to note that 
the calculated values extrapolated to A' = 0 give 
Cd = 0.76 for the cylinder and 0.27 for the hemi- 
sphere. 

The formation of an enveloping cavity has a 
particularly effective stabilizing influence on blunt- 
nosed bodies. In the case of both the square-end cyl- 
inder and the truncated ogive, the “bullets” tested 
were dynamically unstable in the water as long as 
cavitation was suppressed. The resultant oscillations 
about the support point loaded the model support 
system excessively. With the growth of cavitation, 
however, both bodies quieted down and with the for- 
mation of the full clear cavity shown in Figure 14, no 
oscillations existed and the hydrodynamic forces were 
uniformly steady. 

6.2.6 Drag of a Cylinder in the Cavity 

The two-dimensional case of a circular cylinder 
aligned with its axis normal to the flow was investi- 
gated also. A M-in. diameter rod spanning the 14-in. 
diameter working section of the water tunnel was 
tested at velocities of 47.5, 50, and 55 fps for a range 
of the cavitation parameter that assured a well-de- 
veloped cavity. A line made by inlaying a 0.010-in. 
wide copper strip extended along the length of the 
rod so that with the aid of the balance mechanism for 
yawing models, the rod could be turned about its 


THE EFFECT OF CAVITATION ON DRAG 


145 



Figure 16. Three-quarter-inch diameter circular c\4inder in cavity. 


146 


FORCES RESULTING FROM CAVITATION 


axis and the angular position of the separation point 
observed. 

Photographs showing the end view of the spindle 
and the cavity outline as seen through the top trans- 
parent window of the working section, and simultan- 
eous side views showing the length of the spindle are 
presented in Figure 16. 


separation point apparently makes a small rearward 
shift as the cavity wall clears and then moves for- 
ward again. This behavior agrees qualitatively with 
the observed decrease in cavity width. The angle of 
separation measured back from the stagnation point 
falls between approximately 76 degrees and 80 de- 
grees for the range of K from 0.45 to 0.80. 


Description of Cavity 


Drag Versus K 


It is seen that for the early stages of cavitation the 
bubble surface is opaque and milky, and is composed 
of the so-called fine-grained cavitation. At a critical 
K of about 0.50, however, the cavity wall suddenly 


1 



















y 












CAL 

.cuu 

WED 

FRO 

iJS 

ISTR 

M 

OF 








-ME^ 

^SUREME^ 
PRESS D| 






































X 

47.5 

FT/ 

'SEC 









+ 

o 

50 FT/SEC 
55 FT/SEC _ 










M 

L_ 









0 0.Z 04 06 0.8 10 \2 

CAVITATION PARAMETER, K 


Figure 17. Drag coefficient for ^-in. diameter circu- 
lar cylinder. 


becomes clear and transparent. This is indicated by 
the glossy texture of the cavity shown in the bottom 
photograph. At the same time the width of the cavity 
is reduced somewhat, as can be seen by comparison of 
the end views of the spindle for K = 0.50(+) and 
0.50( — ). Note also that the cavity boundary extend- 
ing back from the point of separation at the cylinder 
is sharply defined by a clear-cut line after the transi- 
tion occurs. In the side view photographs, the separa- 
tion of the flow at the cylinder surface is indicated by 
the irregular line in the center of the highlight. Ahead 
of this highlight the forward portion of the cylinder 
is shown in dark relief, while downstream from the 
highlight the cylinder is enveloped by the cavity and 
cannot be seen until the cavity wall becomes trans- 
parent as in the bottom photograph. The point at 
which the flow separates from the cylinder surface 
was observed to shift forward slightly towards the 
stagnation point as K is reduced. At the critical K the 


Figure 17 shows measured drag coefficients and 
theoretical coefficients calculated from wind-tunnel 
measurements of pressure on the cylinder surface. 
As predicted by the theoretical values, the measured 
Cd decreases with increasing cavitation. The varia- 
tion is approximately linear down to the critical K 
when the trend of the measurements changes sharply. 
The lower Cd value after the transition to the clear- 
walled cavity is also consistent with the observed de- 
crease in cavity width. The measurements show Cd 
to fall below the theoretical curve as K is reduced 
further and the cavity elongated. However, the ac- 
curacy of the measurements in this region is question- 
able because of the difficulty with the accumulation 
of air in the tunnel working section. 

Comparison with Calculated Cd 

Above the critical K the curve of measured drag 
coefficients parallels the theoretical curve but shows 
higher values. The theoretical coefficients were cal- 
culated using equation (3). The limits of integration 
of the pressure intensity term were determined from 
assumed points of separation from the cylinder sur- 
face. For the limiting condition of A = 0, separation 
was assumed to occur where the dimensionless pres- 
sure term (P — Po)/(pt^^/2)becamezeroforthewind- 
tunnel determinations. For higher K’s (less cavita- 
tion) separation was taken to occur where the reduc- 
tion in pressure below Pq gave values of (P — Po)/ 
(py2/2) equal to assumed values of K. This method 
indicated separation points much farther forward 
than actually measured, which causes the lower the- 
oretical drag coefficient curve shown in Figure 17. 
Such a discrepancy in the point of separation is not 
unexpected because the flow with a cavity is actually 
quite different than the noncavitating flow in the 
wind tunnel. With the cavity some change in the 
pressure distribution on the part of the body must be 
necessary to provide the extra forces required to 
open up the cavity. 


THE CROSS FORCE AND MOMENT IN THE CAVITY 


147 


Wall Effects 

Some deviations from the truly two-dimensional 
case exist. There is a small wall effect because the cyl- 
inder occupies 7.3 per cent of the tunnel cross section. 
Also, the ratio of channel width to the cylinder di- 
ameter is 19 to 1 at the maximum section, but is re- 
duced towards each end of the cylinder. The change 
is slow, however, so that all of the cylinder except the 
extreme end is at a good distance from the wall. 
Probably the boundary layer caused by the tunnel 
wall, which is of the order of in. thick, will have a 
predominant influence in this zone. Thom^® reports 
that the presence of channel walls parallel to the axis 
of a cylinder causes a correction to the velocity of the 
order of 1 per cent for a ratio of channel width to cyl- 
inder diameter of 20 to 1 and less than 2 per cent for a 
ratio of 10 to 1. It is unlikely that a ratio of 19 to 1 
for the circular tunnel cross section will cause a cor- 
rection greater than the 2 per cent for the 10-to-l 
ratio with parallel walls. 

Alternating Forces 

The measurements shown in Figure 17 were con- 
fined to cavitating conditions because, without the 
cavity, excessive lateral vibration of the cylinder pro- 
hibited operation at these high velocities. This was 
due to the alternating cross force resulting from the 
shedding of vortices of the von Karman trail. But 
with the cavity completely stable conditions were 
obtained, permitting operation at even the maximum 
velocity of the water tunnel. To get to the high ve- 
locity without vibrations severe enough to damage 
the balance equipment, it was necessary to cause the 
cylinder to cavitate at low velocities and then to raise 
the speed while maintaining the cavitation bubble. 
An indication of the alternating forces of the vortices 
generated for noncavitating flow is given by the ob- 
served lateral deflections of approximately Ke in. at 
25-fps velocity. A uniform static load of about 8 psi, 
or a total of about 110 lb, is necessary to cause this. 
With cavitation at 58 fps, as shown in the top picture 
of Figure 16, a deflection was observed only in the 
direction of motion. A maximum deflection of the 
order of 34 in. (34 of the cylinder diameter) for a 
measured total drag of 150 lb was obtained. The de- 
flection in the direction of motion can be seen in the 
top views of the cylinder by comparing the position 
of its axis with the neutral position indicated by a line 
drawn between the two arrow points. Note that the 


maximum deflection is obtained in the top photo- 
graph for the highest K. This deflection also accounts 
for the inclination of the cylinder observed in the side 
views. 

Noncavitating Drag 

Measurements were obtained for noncavitating 
conditions in a velocity range of 10 to 25 fps, or a 
Reynolds-number range of 55,000 to 160,000. Cd was 
constant and equal to 1.13 ±0.03. This agrees with 
published data on the drag of a cylinder of infinite- 
aspect ratio. 


6 3 the cross force and moment 

IN THE CAVITY 

6.3.1 Effect of Body Shape on Cavity 
Cross Force and Moment 

Cavity Symmetry versus Nose Shape 

The spherical-tipped noses shown in Figure 13 have 
the common characteristic that the cavitation bubble 
is formed by separation of the flow well forward on 
the tip so that water is in contact with only a portion 
of the spherical segment. The bubble shape should 
therefore be independent of yaw as long as the after 
part of the body does not reach over and touch the 
cavity walls. Top views of these same noses in fully 
developed cavitation bubbles are shown in Figure 18 
yawed at 3 degrees. Note that in each case separation 
occurs along a sharp line normal to the direction of 
motion, and the resulting cavity, while displaced 
laterally as viewed from above, is symmetrical about 
a line parallel to the flow. In the case of the 5-caliber 
by 76-degree spherogive the cavity does not com- 
pletely envelop the body, yet it retains its symmetry 
back to a point where it intersects the body sur- 
face. 

In contrast, the shapes shown in Figure 14 all pre- 
sent an asymmetrical obstruction to the flow when 
yawed. Consequently, separation of the flow cannot 
occur symmetrically and the resulting cavity must be 
asymmetric. Views of cavitation bubbles in Figure 19 
formed by these noses in yawed positions show this 
effect clearly. The cavities for the two blunt noses 
have trailing bubbles displaced slightly in the direc- 
tion of yaw, while the ellipsoid has a trail of bubbles 
displaced slightly opposite to the direction of 
yaw. 


148 


FORCES RESULTING FROM CAVITATION 


Forces versus Cavity Symmetry 

The characteristics which determine whether or not 
the bubble is symmetrical are important in deter- 
mining the hydrodynamic forces that will act on the 
body under yaw. Since the resultant force must be 
equal and opposite to the momentum change of the 
water deflected by the body, the sj^mmetry or asym- 
metry of the cavitation cavities determines the exist- 
ence and sense of moment and cross force. Thus, for 



MK 13 K = 0.30 



2.3X78*’ SPHEROGIVE K = 0.26 



5 X 76“ SPHEROGIVE K = 0.22 


Figure 18. Cavitation bubbles on spherical-tipped 
noses. Yaw = 3 degrees. 

the spherical-tipped noses used in these experiments, 
the cross force should become zero and the moment 
should be due only to the drag acting through the 
center of curvature of the spherical segment forming 
the nose tip. On the other hand, a finite cross force 
should exist on the other noses, causing a definite up- 
setting or destabilizing moment in the case of the 
ellipsoid, with a stabilizing moment tending to 
counteract the destabilizing effect of the drag in the 
case of the blunt noses. 

Measured Coefficients 
The cross force and moment coefficients Cc and Cm 


measured for these noses are shown in Figure 20, 
plotted as functions of the cavitation parameter /v. 
The moment coefficients are calculated for direct 
comparison with the coefficients for a reference pro- 
jectile 7.18 calibers long with the center of gravity at 
42 per cent of the length back from the nose tip. 
The data are not corrected for support interference 
effects because it was found that the effect, if any, on 
the cross force C and moment M was very small 
once the full cavity was developed. On the other 
hand, as the curves indicate, both C and M are 
much larger just before the cavity is formed than 



2 1/2:1 ELLIPSOID 


Figure 19. Cavitation bubbles on flat-faced and ellip- 
soidal noses. Yaw =3 degrees. 

after. Since the values for other than the cavity 
stage are of significance only for indicating trends, 
no corrections were made. 

In general, the trends shown by the curves as K is 
reduced and the test conditions approach a full cav- 
ity verify the qualitative deductions just stated. The 
hemisphere nose on which a big cavity was developed 
at the K’s of the test shows zero cross force and a 
moment for normal cavitation-free operation of about 
% that of the reference projectile without fins, or 
about }/i of that of the reference projectile with fins. 
This measured moment can be approximated with 
fair accuracy from the drag measurement. For the 
2.3-caliber by 78-degree spherogive, the cross force is 
finite but very small, and the moment is also reduced 
from the cavitation-free value of the reference pro- 
jectile. Both Cc and Cm are decreasing rapidly with 








THE CROSS FORCE AND MOMENT IN THE CAVITY 


149 


increasing bubble size so that in the light of the ob- 
served bubble symmetry in Figure 18, it is probable 
that Cc will eventually become zero. 

For the other two spherical-tipped noses, the Mark 
13 and the 5-caliber by 76-degree spherogive, both 
show relatively high cross force and moment. This is 
attributed to the extra length of these noses and the 
difficulty of getting a cavity large enough to assure 
no interference at points aft of the separation zone. 


— r 

— 1 

itn 

1 — 1 

•SP 

1 1 

HERO 

IGIVE 

V 










0 




// 

- 


ELLI 

1 1 

IPSO. 

0 




s 

a 

-1 




7 


^ 2 .: 

S X 

78* < 

• ' 

1 1 

iPHEF 

1 

»OGI\ 

/E 



CD' 


MK 1 : 





YAW 

‘HEMISPHERE 











►3* ' 

AW 





















0 

Z 








5QUA 

RE E 

>10 

CYU^ 

lOER 


□ 

»i. 














ao4 








/ 

1 

,A»K 

1 

13 







5x7( 

>• SI 

»HER( 

XavE 


/ 













/' 











4=1 

ELL 

IPSO 

A 






OGIV 





ID^ 

> 


3 X 78 SPHER 
1 1 

E 







y 

/ 

/ 

+3 I* yAw 

1 1 









X 


'c 

-HE 

MISP 

HERE 











3* Y, 

kW 




























^SQUAR 

E END CYLIN 

DER 









1 



r 



02 03 04 05 Gl6 

CAVITATION PARAMETER, K 


07 


Figure 20. Effect of nose shape on moment and cross 
force in the cavity. 


This is especially severe in case of the spherogive be- 
cause of its high resistance to the inception of cavita- 
tion. A similar result was obtained with the hemi- 
sphere nose when the bullet was elongated to the 
point that there was some question as to whether the 
cylindrical portion interfered with the cavity wall. 
By shortening the bullet, however, this was elimi- 
nated. It is not possible to assemble these two noses 
in shorter units so the results from these tests are in- 
cluded with this reservation. The trend shown is con- 
sistent, however, with the symmetry of the cavita- 
tion bubble, and Cc should eventually fall to zero for 
both units. 


The 23 ^-to-l semiellipsoid nose also results in high 
Cc and Cm but for different reasons. While the cavi- 
tation pictured in Figure 19 is well developed, the 
cavity is not formed by clean-cut separation as on the 
spherical-tipped models. Instead, the coarse-grained 
cavitation bubbles appear intermittently over a 
broad zone on the nose surface, and form a close-fit- 
ting sheet over the surface of the body. In a sense, 
therefore, a cavity is not really formed on this shape. 
As a result, the trailing bubble is inclined to the di- 
rection of flow, and in light of this asymmetry, it is 
not expected that Cc will vanish or that Cm will be 
reduced to the low value shown for the hemi- 
sphere. 

The square-end cylinder produces both a cross 
force and moment that is stabilizing in effect. This is 
because the pressure on the flat face acts normal to 
the face and, hence, has a lateral component tending 
to reduce the angle of yaw. But for asymmetry in the 
pressure distribution across this face, the resultant 
vector would coincide with the axis of the cylinder 
and zero moment would result. The existence of a 
small moment is an indication of a slight shift in the 
stagnation point in a direction opposite to the sense 
of the yawing. 


6.3.2 Cross Force and Moment 

on a Complete Projectile 
during Cavitation 

Description of Cavities 

It will be recalled that the projectiles pictured in 
Figures 9, 10, and 11 are equipped with three of the 
spherical-tipped noses just discussed. Figures 21, 22, 
and 23 show additional pictures of these same pro- 
jectiles for more advanced stages of cavitation. The 
same characteristics observed in the photographs of 
the short bullets are observed when these shapes are 
used with a full body. Separation occurs on the spher- 
ical segment along a clear line which is normal to the 
flow. Consequently, the bubble is formed with an 
initial symmetry. This symmetry is maintained back 
to the point where the body and tail slice through the 
bubble interface. For the 5-caliber by 76-degree 
spherogive the higher resistance to inception of cavi- 
tation results in less bubble growth at the same value 
of K than for the hemisphere or the standard Mark 
13, so that at A = 0.25, the nose bubble is scarcely 
more developed than at A = 0.35 on the hemisphere. 


150 


FORCES RESULTING FROM CAVITATION 


Even for the partially developed conditions shown, 
however, separation occurs along a line normal to the 
flow on the spherical tip of the nose. 


Measured Coefficients 

Measurements of the cross force and moment co- 
efficients for these three models are shown in Figure 



K= 0.26 


Figure 21. Hemisphere nose on Mk 13-2 torpedo. 

Yaw = 3 degrees. Top and side views. 

24. Because these measurements include primarily 
the intermediate range between no cavitation and 
complete cavitation, corrections for support inter- 
ference are necessary, if the results are to be com- 
pared with the corresponding values without cavita- 
tion. The results show that for the advanced stages 
obtained on the hemisphere and Mark 13 noses, a 
zero or stabilizing moment is obtained. There is also a 
tendency for the cross force to be reduced. In these 
cases the stabilizing effect is caused by the tail and 
afterbody “biting” into the water and overcoming 


the very small destabilizing effect of the nose. The 
latter, according to the measurements on the short 
bullets, is reduced once most of the nose is enclosed in 
cavitation, thus contributing also towards a stabiliz- 
ing trend. The curves also show a tendency towards a 
reduced cross force when the bubble is well developed. 
It will be noted by comparing the photographs in 



K=0.22 


Figure 22. Standard Mk 13 nose on Mk 13-2 torpedo. 

Yaw = 3 degrees. Top and side views. 

Figures 21 and 22 that a larger cavity is obtained on 
the hemisphere than on the Mark 13 at the same 
values of K. Thus the hemisphere results in a more 
pronounced effect on the cross force and moment as 
shown. These curves extend to a high enough K to 
include also the noncavitating performance and the 
effect of the initial stages of cavitation on the per- 
formance. In the case of the hemisphere and the 
Mark 13, both the cross force and the moment drop 
off with the onset of cavitation on the nose and on the 
tail structure. As cavitation develops the cross force 


SUMMARY OF OBSERVATIONS AND CONCLUSIONS 


151 


increases again to slightly above its noncavitating 
value. Apparently there is a differential effect so that 
the increase is greater at the nose, because the mo- 
ment begins to increase slightly at the same time. 
With continued growth the distorted flow pattern 
causes a complicated additional fluctuation of both 
C and M until the cavitation envelops most of the 
body. At this stage the reduced moments and cross 



K = 0.25 


Figure 23. Five caliber by-76-degree spherogive nose 
on Mk 13-2 torpedo. Yaw = 3 degrees. Top and side 
views. 

forces already mentioned are obtained. The curves 
for the 5-cahber by 76-degree spherogive nose begin 
at A = 0.72 when cavitation is already present on 
the tail structure. The nose does not begin to cavitate 
until K is approximately 0.42. At the lowest K of the 
tests, and the maximum bubble development. Figure 
23 shows that nose cavitation is still confined to the 
lee side of the body although there is strong cavita- 
tion on the afterbody and the tail. For these conditions 
both moment and cross force show a tendency to 
drop off. This is more pronounced in the case of the 


moment which is caused primarily by the high drag 
of the tail. 


6 ^ SUMMARY OF OBSERVATIONS 
AND CONCLUSIONS 

The main findings of the investigation of the forces 
and moments acting during cavitation are summar- 
ized as follows: 

1. There is no sudden rise in the drag coefficient 
with the inception of cavitation. 

/0.4 

I 

u 

8 
















»76’< 

>PHER( 

_sJ 






/ 

i 

1 .-v 







MK 13' 






1 

r 

A 

-HEMISPHER 

1 i 

E 

1 

















,MK 13 

> 






S 






!' 

/ 




5 X 7i 

>• SPK 

IER06I 

VE 



/ 

1 

/ 









1 

1 

1 

/ 

-HEM 

ISPHEI 

RE 







/ 

1 

1 

1 








/ 

1 

1 

f 










1 

1 








® 0 02 0.4 0,6 Q8 1.0 

CAVITATION PARAMETER, K 


Figure 24. Effect of cavitation on moment and cross 
force of ring tail projectile with three different noses. 
Yaw = 3 degrees. 


2. Enough cavitation must develop to alter ap- 
preciably the normal flow pattern before the drag is 
affected materially. When this occurs the amount of 
cavitation as observed visually occupies an appreci- 
able physical volume. 

3. Between inception and the marked increase in 
drag the coefficient may increase slowly, may remain 
unchanged, and in some cases has been observed to 
decrease slightly. 

4. A qualitative comparison between cavitation 
and separation indicates: 

a. For blunt bodies with severe separation under 
noncavitating conditions the appearance of 


152 


FORCES RESULTING FROM CAVITATION 


cavitation does not immediately alter the flow 
pattern around the body, and hence intro- 
duces no immediate effect on Cd. 
b. For other bodies with a normal boundary 
layer, cavitation and local separation both 
have the same basic effect on the flow in the 
boundary layer, and hence on the skin friction 
components of Cd. 

5. As cavitation develops beyond the inception 
point, the skin friction component is probably re- 
duced because there is less high-velocity fluid in con- 
tact with the surface. 

6. Drag is proportional to the change in mo- 
mentum imparted to the water so that at a given 
value of Ky drag in the cavity is proportional to the 
bubble size relative to the diameter of the body. For 
a given body, as K is reduced the cavity drag coeffi- 
cient decreases, although the cavity size grows, be- 
cause the momentum required to form the cavity is 
reduced in proportion to the pressure forces, repre- 
sented by (Po — Pb) which must be overcome. 

7. For the square-end cylinder and hemisphere, 
Cd in the cavity agrees within a few per cent with 
values calculated from the measured pressure dis- 
tribution. 

8. The effect of rounding the corners on noses with 
sharp edges, such as obtained with a flat face, results 
in a smaller cavity and less drag. For the case of the 
truncated ogive with rounded edge, Cd in the cavity 
is reduced to about % the value calculated for a 
sharp edge. 

9. Cross force and moment depend upon the cavity 
shape and hence upon the shape of the wetted portion 
of the body. 

10. With spherical-tipped noses proportioned so 
that the cavity always separates on the spherical 
segment, not only at zero but at the maximum yaw, 
the cross force is zero and independent of yaw, and 
the moment is caused by the drag only. 

1 1 . With bodies which do not have spherical- tipped 
noses, the cavity produced is asymmetric and a 
definite cross force exists. 

The sense of this cross force depends on the sign 
of the lateral momentum imparted to the water, and 
hence on the direction of the cavity asymmetry. 

12. With a complete projectile a reduced cross 
force and a zero or stabilizing moment are obtained 
when most of the body is enveloped in a cavity, 
but the tail projects through the cavit}^ wall into 
the water. 

13. For intermediate stages between full and no 


cavitation the growth of cavitation alters both the 
cross force and the drag contributions from various 
parts of the projectile body. 

The shift in magnitude, direction, and point of 
application of the resultant hydrodynamic force 
causes simultaneous variations in Cm. 


6 5 REMARKS ON APPLICATION OF 
OBSERVATIONS AND CONCLUSIONS 

The basic problems around which this research has 
centered have been connected with underwater pro- 
jectiles and consequently applications of the results 
to this field are most direct. Consider first the normal 
underwater operation of high-speed torpedoes. 

High-Speed Torpedoes 

Cavitation is known to be detrimental and in the 
absence of definite information regarding the limits 
of its effect, every effort is normally made to keep the 
operating velocities below those for incipient cavita- 
tion. However, the present results show that appreci- 
able cavitation can be tolerated on typical torpedo 
shapes before the drag increases as much as 10 per 
cent. In the examples shown in Figures 5 and 8 an 
increase of about 10 fps or 10 to 15 per cent above the 
cavitating velocity was allowable. Thus it may easily 
be worth some sacrifice in power to increase the speed 
by such an amount. Admittedly, the simultaneous 
effect of cavitation on the cross force and moments 
can not be ignored. For example, normal operation 
with a negative buoyancy calls for an angle of attack 
to support the load. Since the torpedo shape with the 
hemisphere nose in Figure 8 showed about a 10 per 
cent loss in cross force at 3 degrees yaw for the same 
K at which the drag increased 10 per cent, cavitation 
could cause difficulty in maintaining the proper 
depth. With the decrease in cross force (lift in the 
vertical plane), the depth mechanism would operate 
the rudders to give the body the increased angle of 
attack necessary to carry the load. This trend would 
persist until a new set of equilibrium conditions was 
obtained. Under these conditions higher drag would 
result. Variations in the moment and cross force will 
result in other variations in maneuverability. For ex- 
ample, the turning radius will be rather unpredict- 
able if excessive cavitation exists, so that behavior 
on angle shots will not be consistent. The selection of 
shapes for the projectile components such that cavi- 


^CUiMlI>EATL\£ ? 


APPLICATION OF OBSERVATIONS AND CONCLUSIONS 


153 


tation occurs as uniformly as possible on the lee and 
windward sides will tend to reduce the unbalanced 
effect on the hydrodynamic forces. 

All these effects are particularly serious when the 
projectile operates without much submergence and K 
is correspondingly reduced. In fact, for very low sub- 
mergence, cavitation will occur first on the top side 
of the projectile even with no angle of attack. A tor- 
pedo seeking depth can easily be subjected to inter- 
mittent cavitation as it rises and falls along its course 
and the resultant unbalance in hydrodynamic effect 
should certainly contribute to delay in reaching 
equilibrium conditions. It is possible also that cavita- 
tion of this type could increase the oscillations of the 
projectile and make it break surface. 

Air- Water Entry 

Reference has already been made to the similarity 
of cavitation bubbles to the cavities obtained at air- 
water entry. A basic difficulty in translating these re- 
sults to entry problems is the unsteady character of 
the latter. However, qualitative conclusions can still 
be used to obtain some useful concepts regarding the 
effect of shape and consequent cavitation develop- 
ment on the behavior at entry. The most obvious 
application is the effect of nose shape in the cavity on 
cross force and moment, and hence on the tendency of 
the projectile to yaw and drift. The spherical- tipped 
noses, of which the spherogive series is typical, have 
the special properties of giving zero cross force, if 
proportioned to assure separation of the cavity on 
the spherical segment. In this case the only moment 
is that due to drag. Blunter noses, it was observed, 
actually produced a large stabilizing cross force and a 
resulting moment that overcomes the effect of the 
drag and thus results in a net stabilizing moment. It 
should be possible to design a nose shape slightly 
blunter than a hemisphere which would produce a 
similar effect and make Cm stabilizing or equal to 
zero within a desired yaw range. Cavitation charac- 
teristics which are better than those of the hemi- 
sphere at inception and during the early stages of 
development have been obtained for a shape differing 
only slightly in size or volume from a hemisphere, by 
making the slope and curvature of the surface profile 
continuous over the nose proper and at the junction 
between the nose and the cylindrical body. With 
judicious treatment of the profile up to the zone of 
separation at least, good results should also be ob- 
tainable for the cavity stage. The insensitivity of 


moment and cross force to yaw will contribute to- 
ward less sensitivity to yaw or pitch at entry, and 
tend to reduce deflections from the set trajectory 
during the cavity stage. 

Any nose shape should be investigated for its be- 
havior on impact at entry, since the projectile breaks 
the surface with one side of its nose, resulting in a 
nonsymmetrical cavity and nonsymmetrical forces in 
this stage. However, qualitative conclusions for this 
condition can be obtained also from steady-state 
cavitation data since, neglecting the additional ap- 
parent mass effects, the sense and point of application 
of the resultant forces immediately after impact must 
be the same as the corresponding forces measured 
with a large cavitating bubble. If the launching con- 
ditions are such that the whip or pitching velocity 
induced on impact is serious, the shape of the initial 
cavity formation, and hence the forces acting on the 
projectile, can be modified by changing the nose 
shape. This procedure has been tried to some extent 
on full-size torpedoes.^® 

The existence of moment and cross force in the 
cavity results in two well-known effects. First, the 
moment causes the projectile tail to go to one side of 
the cavity where it sticks through the bubble until 
enough stabilizing moment is built up to offset the 
destabilizing moment from the nose. Second, the 
cross force produces a lateral motion of the center of 
gravity and causes a curved trajectory. It has been 
reported^^ that even for long projectiles the resultant 
curve is dependent primarily on the nose shape. 
Hemispherical noses cause little cross force and the 
curvature is practically infinite. Noses with sharper 
ogives than 2.0 calibers result in large cross forces and 
short radii of trajectory curvature. The beneficial ef- 
fect on drag in the cavity of reducing the area con- 
tacted by the water is well known. This idea has been 
applied to blunt-nosed projectiles particularly where 
the reduction in drag is appreciable. Spherogives and 
other combination forms can be used to produce the 
same effect with basically low-drag shapes. 

Lifting Surfaces 

The loss of lift and increase in drag associated with 
the onset of cavitation is a serious problem in appli- 
cations to lifting surfaces of various types. The fixed 
and adjustable guide surfaces on projectiles, sub- 
marines, and surface ships are vulnerable to cavita- 
tion, particularly for conditions of yaw such as ob- 
tained during a maneuver. The shroud ring tail on 


154 


FORCES RESULTING FROM CAVITATION 


the typical torpedo already discussed is one example. 
Movable rudders of course are the most likely to cavi- 
tate, and in some cases can be rendered quite in- 
effective by large cavitation zones. In general, it is 
probable that there will be less loss in lift if the cavi- 
tation is of the coarse-grained type and the develop- 
ment of a full cavity on the low-pressure side of the 
surface can be avoided. 

Hydraulic Machinery 

Pumps, turbines, and propellers are basically lift- 
ing surfaces that are also subjected to cavitating con- 
ditions. In general, cavitation causes a loss of head 
or thrust and torque. However, an actual increase in 
head, torque, and efficiency has been observed with 
the onset of cavitation in some radial-flow type 
pumps.^^ It has been suggested that this effect is 
caused by a slight reduction in skin friction as cavi- 
tation grows. The effect of vane shape controls this 
behavior, just as in the case of the three-dimensional 


bodies investigated. Shaping the vanes to give coarse- 
grained cavitation should prove beneficial on two 
counts. First, inception should be delayed, since it 
was the more highly resistant forms that gave this 
type of bubble formation. Second, with the more ad- 
vanced cavitation there probably will be less loss in 
lift on the blades. 

In the case of pumps and turbines, the ‘‘lattice’’ 
effect of the vanes will modify the cavitation be- 
havior over that obtained with a single blade. The 
modifications are similar to “wall effects” obtained in 
the water-tunnel tests, but of great magnitude. The 
main deviations will be in the advanced stages of 
cavitation where the vapor occupies an appreciable 
fraction of the total volume between blades, and 
hence seriously restricts the water passage. For the 
initial stages the concepts presented here of the 
similarity between the effects of cavitation and sep- 
aration on the boundary layer and, hence, on the gen- 
eral flow around the blade should apply with good 
accuracy. 




Chapter 7 

CAVITATION NOISE FROM UNDERWATER PROJECTILES 


7 1 PURPOSE AND SCOPE OF 

NOISE MEASUREMENTS 

T he sonic and supersonic noise emitted during 
the onset and development of cavitation on 
various parts of underwater bodies has become im- 
portant for several reasons. For example, the noise 
produced by a cavitating propeller on a ship is easily 
detected and the ship’s position ascertained by under- 
water sound locating devices. On the other hand, if 
the vessel carrying the sound gear has a cavitating 
propeller, the noise produced interferes with the 
operation of the listening equipment. The importance 
of this cavitation noise in connection with other 
acoustical applications can be visualized readily. It 
was the purpose of the investigations in the water 
tunnel to measure the noise produced in the 20- to 
100-kilocycle frequency range by certain body shapes 
and to determine the variation of sound emitted with 
the beginning and growth of cavitation. A further aim 
was to determine, if possible, the distribution of the 
noise in the various frequency bands. In addition an 
investigation was made to identify the exact location 
of the source of the sound during cavitation.i’^ 
High-frequency noise measurements were possible 
in the water tunnel working section because, al- 
though the circulating pump and other associated 
equipment produced a high noise level in the range of 
sonic frequencies, they produced but few high-fre- 
quency components. Consequently, the tunnel cir- 
cuit was “quiet” in the range above 6 kilocycles. 

7 2 THE APPARATUS 

The noise measurements were made in the working- 
section of the water tunnel using the regular 2-in. di- 
ameter models mounted on a streamlined strut. The 
hydrophone and recording equipment used is the 
same as that described in Section 2.8. Two sys- 
tems of mounting the receiving hydrophone were used. 
In one case the hydrophone was placed in a water- 
filled plastic blister clamped to the Lucite window of 
the working section as shown in Figure 1 . The second 
method made use of focusing reflectors or “mirrors” 
in connection with the hydrophone, with both the 
mirror and hydrophone submerged in a water-filled 


tank attached to the side of the working section. 
Photographs of this arrangement with spherical and 
ellipsoidal reflectors are shown in Figures 2 and 3. 
Provisions were made for directing and focusing the 
h 3 ^drophone mirror assembly from any position with- 
in the side tank. Except for the Lucite window both 
arrangements provide a continuous water path from 
the noise source to the hydrophone, or to the re- 
flecting surface and back to the hydrophone. 

The focusing s 3 ^stem has the advantages of increas- 
ing the gain at the hydrophone, and limiting the re- 
ception from other than the focused direction, thus 
tending to reduce possible interference from other 
sound sources and from sound reflected from the 
tunnel walls. Typical directional characteristics of 
the reflector system^^ are shown by the directivity 
patterns of Figures 4 and 5 which are for the hydro- 
phone alone and the hydrophone with an ellipsoidal 
reflector.^ The directivity 'pattern is a polar diagram 
showing the sound pressure, in decibels relative to 
that on the axis of symmetry of the mirror, measured 
for different angles between the noise source and the 
axis of symmetry. While the hydrophone alone shows 
but slight directional characteristics, the addition of 
the ellipsoidal reflector gives a directivit 3 ^ index of 
— 28 db at 50 kilocycles and —31.4 db at 70 kilocycles. 
The directivity index, which can be calculated from 
the three-dimensional directivity patterns of the 
hydrophone system, is the ratio in db of the acoustic 
pressure averaged over all directions to the pressure 
measured on the axis of symmetry. These calibra- 
tions, made with a fixed distance between the noise 
source and the focal points of the reflectors, dupli- 
cated the geometrical arrangement used for the 
water tunnel tests except that the Lucite window 
between the source and the receiving hydrophone was 
not included. This window has a flat outside surface 
and concave cylindrical inside surface. A comparison 
of the free-field directivity patterns obtained from 
measurements with and without the Lucite window 
is shown in Figure 6. Very little distortion is caused 
by the Lucite in the plane normal to the curved in- 
side surface of the window. During the calibrations 
the effect of changing the distance between the noise 

“These calibrations were made by the Calibration Group of 
the University of California, Division of War Research. 


155 


156 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 



source and the focal point of the ellipsoidal mirror 
was investigated also. It was shovm that the focus- 
ing obtained when the noise source moved along 
the axis of symmetry of the mirrors was only 3^ to 


Figure 2. Spherical reflector and hydrophone assem- 
bly focused on projectile inside working section. 

BACKGROUND NOISE 

The measurements of sound from cavitating pro- 
jectiles in the tunnel working section include a certain 
amount of background noise generated by the tunnel 
flow circuit and its mechanical drive. To be sure that, 
over the frequency range of interest, the magnitude 


of this noise was small relative to the cavitation noise, 
a series of measurements was made without the model 
or its supporting strut in the working section. With 
the hydrophone first mounted in the Lucite blister on 
the working section window and later used with the 
mirrors and focused on a fixed point on the tunnel 
axis, noise was measured over a wide frequency range 
for a series of different constant velocities. Examples 
of measurements with the reflectors are given in the 
following paragraphs. Aside from effects on gain due 
to the focusing features of the mirrors, these measure- 
ments are typical for both types of installations. 


Figure 3. Ellipsoidal reflector and hydrophone assem- 
bled in water tank at working section side window. 

Effect of Velocity and Pressure 

The typical curves shown in Figure 7 illustrate the 
magnitude of the background noise and the effect of 
velocity and pressure on the noise. In this figure 
measurements for velocities of 40 to 70 fps are plotted 
as a family of curves of sound pressure in dynes per 
square centimeter (with linear decibel scale) vs the 
cavitation parameter K. The data were obtained 
from tests taken with the spherical mirror focused on 
the centerline of the working section and with the 
sound filters set to include the entire 20- to 100-kilo- 
cycle band. These curves show the same character- 
istic trends as were obtained by the earlier measure- 
ments^’^ without a reflector. For each velocity, as the 
pressure is reduced from an initially high value, the 


Figure 1. Hydrophone mounted in water-filled blister 
on side of working section. 


as good as when the source moved normal to this axis 
and that the best focusing along the axis of symmetry 
was obtained when the sound source was slightly 
short of the conjugate focus of the ellipsoid. 


BACKGROUND NOISE 


157 


increased cavitation and flow separation in various 
parts of the flow circuit caused an increase in noise 
until at a low K a peak is reached and the level drops 
off. The sudden reduction in noise level shown in this 
figure coincides with cavitation in the contracting 
nozzle at the entrance to the working section, and an 
accumulation of vapor and air bubbles which clouded 
the working section and probably acted as sound 
screen between the hydrophone and the noise. 

Effect of Tunnel Circuit Variables 

The data plotted in Figure 7 could be duplicated 
as long as tunnel conditions remained the same. How- 



scale - I RADIAL DIVISION = 5 db 

DISTANCE BETWEEN SOURCE a RECEIVER HYDROPHONE = 16^ IN. 
WATER TEMPERATURE = 68 DEGREES 
DEPTH BELOW WATER SURFACE = 9 FT - 0 IN. 

Figure 4. Directivity patterns for C-llA hydrophone 
in plane normal to hydrophone spindle. 

ever, changes in the condition of the circulating 
pump, in the relative settings of the valves in the 
pressure control circuits auxiliary to the tunnel, or in 
the flow circuit itself, caused some variation in the 
magnitude of the background noise. Differences of as 
much as 10 db have been observed for different com- 
binations of these variables. 

Figure 8 shows the background noise level curves 
olitained with the same spherical mirror assembly 
after an improved contracting nozzle was installed at 
the inlet to the working section. These curves are 
similar to those in Figure 7 but show from 2 db to 5 


db lower noise levels at the same K. The peaks are 
higher, however, because lower JV’s are reached be- 
fore the noise drops. With the original nozzle the 



SCALE - I RADIAL DIVISION - 5 db 

DISTANCE BETWEEN SOURCE 8 RECEIVER HYDROPHONE « 16^ IN. 
WATER TEMPERATURE » 66 TO 68 DEGREES 
DEPTH BELOW WATER SURFACE = 9 FT -0 IN. 

Figure 5. Directivity patterns for C-llA hydrophone 
with 10-in. aperture ellipsoidal reflector in plane normal 
to hydrophone spindle. 



50 KC 90 KC 

SCALE - I RADIAL DIVI90N = 5 db 


DISTANCE BETWEEN SOURCE 8 RECEIVER HYDROPHONE = 16.2 IN. 
DEPTH BELOW WATER SURFACE = 20 FT - 0 IN, 

Figure 6. Effect of Lucite window on directivity pat- 
terns with 6-in. aperture ellipsoidal reflector. Patterns 
are for plane normal to hydrophone spindle and con- 
taining axis of cylindrical surface of window. 

noise was interrupted when cavitation, accompanied 
by an almost simultaneous accumulation of air bub- 
bles, appeared at the nozzle throat. With the new 




158 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 


nozzle, cavitation in the nozzle proper does not occur 
within the experimental range. However, with the 
sustained operation at the low absolute pressures 
corresponding to the lowest K values obtainable, air 
does accumulate in the tunnel and the noise level 
drops. 


ticular test conditions of Figures 7 and 8, and for K 
values above those at which the peaks occur, the 
background sound pressure is approximately propor- 
tional to the fourth power of the water velocity and 
inversely proportional to the hydraulic pressure. Fol- 
low K values nozzle cavitation or air accumulation 
changes this relationship. 


Background Noise Compared with Cavitation 
Noise 

The highest sound pressure measured in the clear 
tunnel was about 420 dynes per sq cm. This was ob- 
tained at 70 fps, which is the maximum velocity at 
which noise from projectiles was recorded. As will be 
discussed later, pressures of 1,000 to 2,000 dynes per 



Figure 7. Background noise level. No model or strut 
in tunnel. Spherical mirror focused on a point on the 
center line of the working section 21 inches from inlet. 
Old nozzle at inlet to working section. 


sq cm were measured with the spherical mirror as 
cavitation developed on the projectile shapes. Since 
the recorded level is approximately the root-mean- 
square value of all the sound contributions, the back- 
ground noise has no significant effect on these pres- 
sures. It is possible also, for the same reason, to ignore 
the relatively small effect of background noise varia- 
tions caused by different tunnel setups as illustrated 
by Figures 7 and 8. 

Similar background noise measurements made us- 
ing the ellipsoidal mirror showed 5 db to 8 db higher 
levels than with the spherical mirror. However, peak 
noise pressures of 5,000 dynes per sq cm or greater 
were measured from cavitating projectiles with this 
reflector, thus making the background noise even less 
significant. It is interesting to note that for the par- 



Figure 8. Background noise level. No model or strut 
in tunnel. Same as Figure 7 except that new nozzle 
installed at inlet to working section. 


2 

o 


g?200 


JOO 

UJ 

I 80 
260 
t 

o 40 
►- 


30 

















SPH 

2 

\ 

ERIC 
*0- 
t = •! 

AL 
100 
50 F 

MIRI 

KC 

T/SI 

ROR 

EC 














































■Tfc 


■o— 

rj 






K - 

• u.ou 








cr 


D"" 





. 











A 


u 



u 



O 

■o 


K = 

■o — 

1.15 




























■120 1 


-115 


-no 


-105 


18 


28 26 24 22 20 

HYDROPHONE POSITION, INCHES 
MEASURED FROM BEGINNING OF WORKING SECTION 


100 J 


Figure 9. Background noise level at different posi- 
tions along center line of tunnel. No model or strut in 
tunnel. 


Uniformity of Background Noise 

A comparison of the background noise obtained at 
different positions along the centerline of the tunnel 
is shown in Figure 9. These measurements were made 
with the velocity and pressure fixed (K = constant) 
by moving the hydrophone and mirror parallel to the 


MEASUREMENTS OF NOISE 


159 


tunnel axis. They show the same noise level through- 
out the length of the working section normally 
occupied the model. 


Background Noise avith Projectile in Tunnel 

In order to verify that these “dear-tunnel” meas- 
urements gave the same background noise that would 
be obtained with actual test installations, a survey 
was made for noncavitating flow with a projectile in- 
stalled in the working section. All the other test con- 
ditions used to obtain the data in Figure 7 were dupli- 
cated as nearly as possible and measurements made 
of noise vs distance along the tunnel axis 2 itv = 40 fps 
and K = 3.74. With such a high value of K no cavita- 
tion existed at any place on the model. These meas- 
urements, shown in Figure 10, gave an average noise 
level within 2 db of the clear-tunnel noise shown for 
the same K in Figure 7. 


MEASUREMENTS OF NOISE 
PRODUCED BY CAVITATING 
PROJECTILES 

Correlation with the Beginning 
and Growth of Cavitation 

Cavitation Types and Influence of 
Profile Shape 

During observations of various projectiles in the 
water tunnel, it was noticed that as cavitation first 
appeared, the formation and collapse of the cavita- 
tion bubbles were different for varying degrees of 
abruptness of the body at the cavitation zone. When 
the profile was not too abrupt, the zone of cavitation 
bubbles appeared to form, grow, and collapse right 
on the surface of the body. For more abrupt bodies 
the bubbles seemed to form at the surface of the body, 
but to spring clear of it before collapsing and disap- 
pearing. For some very abrupt shapes the cavitation 
vapor pocket originated and collapsed in the stream 
away from the disturbing surface, with no visible 
connection to the body itself. Consequently, in 
studying the correlation of sound generated with the 
beginning and growth of cavitation, the several dif- 
ferent forms of cavitation were investigated by using 
several body shapes. The four bodies for which 
measurements are reported here and the type of 
incipient cavitation obtained are: 


1. Hemisphere nose 

2. Semiellipsoid nose 

3. Truncated hemisphere 
nose 


4. Tail rudder tilted 
into stream 


Cavitation forms and collapses 
on the surface of the projectile. 

Similar to hemisphere nose. 

Cavitation vapor bubbles origi- 
nate at the sharp edge but col- 
lapse in the stream away from 
the projectile surface. 

No visible connection between 
cavitation bubbles, which form 
and collapse in water, and the 
rudder surface. 


A comparison of the shapes of the four bodies and 
the types of flow about each for noncavitating con- 
ditions are shown by the scale drawings in Figure 1 1 . 
The three noses and the upturned rudder present to 
the flow successive changes from smooth to blunt and 


= 20 




SEMI-ELUPSOID N(^E TAPER AFTERBy' 


SPHERICAL MIRROR 
20-100 KC 
V = 40 FT/SEC 
K = 3.74, 


LJ. 


CLEAR TUNNEL-. 


l95§; 


I 29 27 25 23 21 19 

HYDROPHONE POSITION, INCHES 
MEASURED FROM BEGINNING OF WORKING SECTION 



Figure 10. Background noise with model in tunnel. 
Semiellipsoid nose. No cavitation. 


abrupt profiles. The flow line diagrams were drawn 
from detailed observations of the actual flow in the 
polarized light flume.® They are useful for determi- 
ning qualitatively the velocity field around the pro- 
jectile and, hence, locating the zones of low pressure 
where cavitation is most likely to occur. Wherever 
the flow, which has been pushed aside by the pro- 
jectile surface, begins to curve back around the body 
(concave towards the body), local reductions in pres- 
sure are affected. The greater this curvature, the 
lower the pressure and the greater the possibility of 
developing cavitation. The flow lines show the maxi- 
mum curvature near the junction between nose and 
cylinder for the hemisphere and semiellipsoid noses, 
at the sharp edge on the truncated hemisphere, and 
at the tip of the rudder on the finned afterbody. In 
addition, the diagrams show varying sharpness in 




160 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 


maximum curvature, indicating earliest cavitation 
for the truncated hemisphere nose or upturned rud- 
der, and later cavitation for the semiellipsoid and 
hemisphere noses. 

Sound Pressure versus Cavitation Growth 

With the hydrophone and spherical mirror focused 
on the zone of incipient cavitation and varying the 
pressure while maintaining the velocity constant, 
measurements showing the variation in sound pres- 




Figure 11. Projectile profiles with flow diagrams. 

sure tvith the stage of cavitation were obtained for 
each projectile. A corresponding series of photographs 
showing the successive stages of cavitation develop- 
ment were also made. All tests were made with zero 
yaw and zero pitch. The results are shown in Figures 
12, 13, 14, and 15 where the sound pressure is plotted 
against the cavitation parameter. A scale for the 
sound level in decibels is also shown. The photo- 
graphs included in the same figures are arranged 
in the order of decreasing values of K and each is 
marked with the corresponding measured sound 
level. Note that in all cases the total sound pres- 


sure in the 20- to 100-kilocycle band is sho^vn, but 
that the data for each nose were obtained at a 
different constant velocity. 

Each set of curves and photographs in Figures 12 
to 15 show the following common characteristics: 

1. With reduction in the cavitation parameter A', 
the sound pressure rises sharply to several times the 
magnitude of the background noise in the tunnel as 
soon as the slightest trace of visible cavitation is 
observed. 

2. The rise in sound begins with the appearance of 
minute cavitation bubbles and reaches a peak value 
while the ring of bubbles is still very narrow. 

3. The sound pressure decreases with continued 
development of cavitation until, for fully developed 
conditions, the noise is but a fraction of the peak 
magnitude. In some cases it drops to approximately 
the same level as the tunnel background noise. 

These characteristics are shown clearly by ex- 
amining Figure 12 for the hemisphere nose. For high 
values of K at which no cavitation occurs on the pro- 
jectile, the measured noise is only that due to back- 
ground disturbances. However, as K is reduced by 
reducing the hydraulic pressure or increasing the 
velocity, and cavitation begins, the noise rises 
sharply to a high value. In this instance the increase 
is from 95 to 1,700 dynes per sq cm, a gain of about 
25 db. With continued growth of cavitation the noise 
peaks and then falls off until, with very large bubbles 
enveloping the body, the measured level equals the 
background noise level. During tests at the K cor- 
responding to Figure 12 A, only small intermittent 
bubbles of cavitation could be discerned by careful 
visual examination. They were too small to be de- 
tected photographically. Figure 12B shows a small 
amount of cavitation along the top half of the body 
at the junction between the hemisphere and the cyl- 
inder. Note that it is a very narrow band, yet as the 
noise curve shows, it is between this condition and 
the slightly more developed one shown in the next 
photograph that the maximum noise is measured. 

Examination of Figure 13 shows the semiellipsoid 
nose to cavitate at a higher K, but otherwise to ex- 
hibit the same characteristics. Because the back- 
ground noise was very low for this 40-fps test, the 
noise gain at the inception of cavitation is nearly 37 
db. Again, as indicated in Figures 13B and C, the 
maximum noise is measured when only a thin ring of 
cavitation appears near the junction between the 
cylindrical body and the nose contour. A second 
small noise peak of undetermined cause is evident at 


MEASUREMENTS OF NOISE 


161 


fet:" K = 079 ^ 

U -SOUND = UNSTEADY 
j. NOISE LEVEL DUE 
TO INTERMITTENT 
CAVITATION 


B 


K = 0.77 

SOUND = 137 DB 




D 


K = 0.68 

i SOUND =138 DB 

I 

r 

\ 

E 


K = 0.65 

SOUND=135 DB 


F 


K = 0.60 

SOUND =130 DB 




* ** * ‘ 111 lit ■ 

29 28 27 26 2 5 24 23 22 21 20 19 « 

DISTANCE ALONG AXIS, INCHES 


K=0.45 

SOUND= 125 DB 


K = 0.4I 

SOUND = 123 DB 


K = 0.31 

SOUND = 115 DB 



* • ‘ ‘ ‘ ‘ ‘ ‘ ‘ 

29 28 27 26 25 24 23 22 21 20 19 18 

DISTANCE ALONG AXIS, INCHES 



Figure 12. Cavitation on hemisphere nose. 


FI m:\TTAE~i 


DECIBELS ABOVE 0.0002 DYNES/ SO CM 


162 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 


A 

K = 2.55 

SOUND = 96 DB 

B 

K= 1.82 

SOUND= 138 DB 

C 


K = 1.74 

SOUND =138 DB 


D 


K = 1.52 

S0UND = 131 DB 


E 

K = 1.29 

SOUND = 129 DB 


F 

K=1.03 

SOUND = 127 DB 


G 




»- « i 1 « ■ - • ‘ * 

29 28 27 26 25 24 2 3 22 21 20 19 » 

DISTANCE ALONG AXIS, INCHES 


I 


K=0.53 

SOUND = NO 
DATA 


J 


K=0.46 

SOUND = NO 
DATA 



K 


K = 0.47 

SOUND = NO 
DATA 




‘ ‘ ‘ ‘ * 

29 28 27 26 25 24 23 22 21 20 19 16 

DISTANCE ALONG AXIS, INCHES 



Figure 13. 


Cavitation on semiellipsoicl nose. 


DECIBELS ABOVE 0,0002 DYNES/SO CM 


MEASUREMENTS OF NOISE 


163 


A 

K = 2.44 

S0UND = 134 DB 

(SEE ENLARGE- 
MENT ON PANEL) 

B 

K = 2.30 

SOUND = 134 DB 


C 

K = 2.14 

SOUND =135 DB 


D 

K = 1,99 

SOUND = 132 DB 


E 

K = 1.83 

SOUND =132 DB 


F 

K = 1.55 


SOUND =128 DB 

G 



K= 1.32 

SOUND = 123 DB 


K = 1.1 9 

S0UND=124 DB 


4-- rr-.i; ' 



I 1 I I . i i t i -4 i * — j 

29 28 27 26 2S 24 23 22 21 20 19 18 

DISTANCE ALONG AXIS, INCHES 


J 

K = 0.82 

SOUND = 119 DB 


K 

K = 0.56 
S0UND = n7 DB 

L 

K=0.53 

SOUND = 117 DB 

M 


K = 0.43 
S0UND=113 DB 


N 

K = 0.33 

SOUND =108 DB 



^ t t i » * 1 till 

29 28 27 26 25 24 23 22 21 20 19 « 

DISTANCE ALONG AXIS, INCHES 



Figure 14 . 


C’avitation on truncated hemisphere nose. 


DECIBELS ABOVE 0.0002 DYNES /SO CM 



164 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 


A 


K= 1.48 

SOUND = 130 DB 


B 

K = 1.38 

SOUND = 132 DB 


C 

K = 1,25 

SOUND » 134 DB 


D 

K = 1.15 

SOUND = 134 DB 

E 

K= 1.03 

SOUND = 134 DB 

F 

K=0.95 

SOUND =133 DB 





29 29 Zf » ti 23 22 Z\ 20 19 18 

DISTANCE ALONG AXIS, INCHES 


J 

K = 0.67 

SOUND =129 DB 

K 

K = 0.65 

S0UND=129 DB 

K 

K = 0.5S 

SOUND =126 DB 



2*9 a 27 X 25 24 23 22 Z\ 20 isi i*8 

distance along axis, inches 



Figure 15. Cavitation on upturned rudder of fin tail. 


DECIBELS ABOVE 0.0002 DYNES/ SO CM 



MEASUREMENTS OF NOISE 


165 


the advanced stage of cavitation shown when K = 
1.03 in Figure 13F. 

Figures 12 and 13 both show similar types of 
incipient cavitation* where the bubbles lay close to 
the body surface. Figure 14 for the truncated hemi- 
sphere nose, shows the second type of cavitation 
where the bubbles collapse in the water away from 
the body. Figures 14A and B illustrate this clearly. 
The trailing ends of the small cavitation wisps which 
originate at the sharp edge on the nose are separated 
from the body by a definite space. With continued 
growth of cavitation, the bubble zone becomes more 
dense and this characteristic is less discernible. The 
same trends in measured sound were obtained as for 
the other two noses with about a 23-db increase in 
level as cavitation began. 

Figure 15 shows sound measurements and photo- 
graphs for a tail rudder tilted up into the stream. As 
the first photographs of the series show, the initial 
cavitation occurs at the rudder post as well as at the 
tip and finally, at very low K values, the entire wake 
behind the tilted rudder becomes filled with vapor. 
The noise curve shows the characteristic increase to a 
peak value and then reduction with cavitation 
growth. Note that, as Figure 15D shows, the peak 
noise, a 40-db gain over the background, is obtained 
with very little visible cavitation. 

It might be noted that surface condition is very 
critical in making the cavitation measurements. The 
noise measurements and cavitation photographs of 
the four noses were made after carefully polishing 
the assembled models and wiping the surface and 
joints between body sections with a waxed cloth. 
These precautions caused the onset of cavitation 
to be more uniform by eliminating early cavitation 
at isolated points around the periphery of the pro- 
jectile. 

Sound Pressure and Bubble Collapse 

The fact that for all three types of cavitation the 
maximum sound was measured when the visible 
cavitation was small, and that the magnitude was 
reduced with the growth of the bubbles, might be tied 
in with the concept that the noise originates primarily 
at the bubble collapse. With small cavitation bubbles 
which form and collapse cleanly and sharply within a 
small physical zone, the energy release and, hence, 
the noise is of high intensity. As the zone of cavita- 
tion grows, the bubbles collapse throughout a larger 
space, and mutual interference and absorption due to 


the damping properties of the bubbles themselves 
reduce the intensity of the noise radiated. 

Comparison of the Four Bodies at Same Velocity 

It should be noted again that each set of data in 
Figures 12 to 15 is for a different velocity and, fur- 
thermore, the inception of cavitation occurs at a dif- 
ferent pressure for each body. Consequently, there is 
no satisfactory basis for comparison of the magni- 



Figure 16. Noise caused by cavitation on four differ- 
ent bodies. 


tudes of the sound levels measured. Measurements of 
the noise produced by each of the projectiles at the 
same velocity of 47 fps were obtained using the ellip- 
soidal reflector instead of the spherical mirror. These 
results are shown in Figure 16. The increased effec- 
tiveness of this reflector over the spherical mirror is 
apparent. For example, the hemisphere nose curve 
shows a maximum sound pressure of 4,800 dynes per 
sq cm for this 47-fps test, as against about 1,100 
shown in Figure 12 for a 60-fps test with the spherical 
mirror. Similarly higher peaks are obtained for the 
others. These curves show some difference in the mag- 
nitudes of the noise peaks for the different bodies. 


166 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 


There is also some difference in the shapes of the 
curves, the peak occurring at a K somewhat lower 
than the inception value for the two most abrupt 
shapes, the truncated hemisphere and the upturned 
rudder. For the hemisphere and the semiellipsoid the 
peak occurs soon after the inception point. For both 
the truncated hemisphere and the upturned rudder, 
the determination of the beginning of cavitation was 
very critical so that sound measurements in that re- 
gion were difficult to obtain. With the other two 
noses, however, the increase, although sudden, could 
be traced, and with extreme care, measurements could 
be made at levels intermediate between the back- 
ground and highest pressures. 

Noise versus Velocity 

Figure 17 shows the change in noise with velocity 
for the hemisphere nose. For the velocity range of 40 



VELOCITY, FT/SEC 

Figure 17. Noise versus velocity. Hemisphere nose. 

to 70 fps the increase in maximum noise for each 
speed is approximately linear. This holds for both the 
20- to 100-kilocycle and 80- to 100-kilocycle fre- 
quency bands. Note also that the ratio of increase 
with velocity is the same, both bands indicating that 
probably the composition of the total noise produced 
at the maximum may be the same at all velocities. 
This maximum noise is not obtained at the same pres- 
sure (submergence) for all speeds, but rather at a 
nearly fixed value of the cavitation parameter If a 
projectile travels under water at a constant depth, 
the maximum noise represented by the straight lines 
in Figure 17 will be generated only at one velocity 
where K assumes the above fixed value. For all other 


velocities the noise will be less than the maximum. 
The other curves in Figure 17 show the variation in 
noise in the 20- to 100-kc band for this nose sub- 
merged to 10 ft and 15 ft. It will be noted that the 
noise level is low up to the critical velocity for the 
inception of cavitation. Then it increases several fold 
until it reaches the maximum level curve. Beyond 
this peak the noise level drops. Cavitation is post- 
poned to higher velocities as submergence increases, 
but when cavitation does occur, the peak noise is 
higher also. It might be noted that the data from 



Figure 18. Movement of noise source with growth of 
cavitation on the hemisphere nose. Compare with Figure 
12C, F, G. 


which these curves were drawn were obtained with a 
different arrangement in the water tunnel setup, so 
the magnitudes of the maximum noise are not 
directly comparable to those illustrated in Figure 
16. 


Note on Magnitude of Measured Noise 

It should be emphasized that the absolute magni- 
tudes of the sound levels measured in the water tun- 
nel bear no particular relation to what might be ob- 
tained in the field. In any event, in either laboratory 
or field measurements the hydrophone receives only 
such a portion of the total sound emitted as the 
geometry of the setup permits. The magnitudes 
reported here are good for comparative purposes 
only. 


MEASUREMENTS OF NOISE 


167 


^ ^ Location of Noise Source 

during Cavitation 

Visible Cavitation and the Noise Source 

It is generally believed that at the point of collapse 
of a cavitation bubble the energy concentration is 
appreciable, resulting in a local pressure intensity 
that is very high. In a collapsing zone the pressure 
waves produced at a very high rate are the cause of 
the mechanical damage commonly known as cavita- 
tion corrosion and of noise, both acoustic and super- 
sonic.^® That the source of noise measured is concen- 
trated at the zone where cavitation is visible is clearly 



Figure 19. Movement of noise source with growth of 
cavitation on the truncated hemisphere nose. Compare 
Figure 14A, F. 

shown by traverses giving the sound pressure as the 
hydrophone is moved parallel to the water tunnel 
axis. As the examples for the hemisphere nose in 
Figure 18 show, the maximum noise level is obtained 
when the hydrophone is positioned to focus on the 
cavitation zone as shown in the photographs of Fig- 
ures 12C, F, and G. At 1 in. on either side of this po- 
sition the sound is reduced 3 to 5 db. The ring source 
shown in the photographs appears as a line to the 
hydrophone receiver so that, as might be expected, 
focusing of the hydrophone in a position 1 in. above 
or below the centerline of the working section gives 
less than 1-db reduction in the level. Because the 
sharpest focusing was obtained at the higher fre- 
quencies the measurements in Figure 18 are for the 
80- to 100-kilocycle band. 


Movement of Source with Shifting Zone of 
Collapse 

If it is assumed that the bulk of the total noise 
measured from a cavitating object is obtained from 
the collapse of the bubbles, the physical observation 
that the collapsing zone moves downstream with the 
growth of cavitation should indicate the downstream 
movement of the noise source. The curves in Figure 
18 also indicate this trend. The peak obtained for a 
cavitation parameter K of 0.56 is approximately 3^ 
in. farther back than the peak for K = 0.73, whereas 



Figure 20. Movement of noise source with growth of 
cavitation on upturned rudder of fin tail. Compare 
Figure 15H, K, L. 


photographs of Figures 12C and G indicate about 0.6- 
in. downstream elongation of the cavitating zone. 

It has been suggested that growth of the sound 
source could indicate an apparent shift in its location, 
or that some combination of the effects of the screen- 
ing and reflections peculiar to the projectile and 
tunnel configuration could explain the measured 
shift. It is felt, however, that the agreement between 
length of cavitation bubble and movement of the 
sound peak measured in this and other cases is good 
evidence that the noise source is moving with the 
zone of the collapsing bubbles. 

Measurements for the truncated hemisphere nose 
in Figure 19 show the same typical trends observed 
with the hemisphere nose. Figure 20 shows the results 
obtained with cavitation on the upturned rudder. 


[ o>Nni)Ki>qTn~j 


168 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 


These curves do not indicate a consistent shift in 
peak, even though cavitation at the lowest K is much 
more severe than at the highest. Reference to Figures 
15H and L shows, however, that the visible zone of 
vapor on the lee of the rudder was changed very little 
as K was reduced. With more severe conditions, 
more and more vapor was entrained by the water and 
swept downstream to collapse outside the range of 
the hydrophone system, but the main cavity shown 
was almost uninfluenced. 

In mounting the hydrophone-reflector assembly 
precise angular adjustment in the horizontal plane 
was very difficult. However, as shown in Figures 2 



Figure 21. Frequency distribution of cavitation noise 
from truncated hemisphere nose. 


and 3, the whole assembly was attached to a carriage 
which, after focusing adjustment, was moved parallel 
to the tunnel axis on machined rails. As a result, while 
the relative portions of the noise peaks were deter- 
mined accurately, the absolute locations were apt to 
be in error by the amount of any angular misalign- 
ment multiplied by the distance between the noise 
source and the hydrophone. For the earliest stages of 
cavitation the location of the peak can be accurately 
checked because the noise undoubtedly originates 
from the very narrow visible band. If all the tra- 
verses are taken without further adjustment this 
correction will apply to all measurements. This pro- 
cedure was followed for determining the absolute 
location of the peaks in Figures 18, 19, and 20. 

The effect of the movement of the sound peak with 
the growth of cavitation has a secondary effect on the 


300 


200 


100 


2 

1 

0-30 

1 

1 KC 








































1 

^YDR0PH0l 
FROM NO 

ME 1 
SE A 


0 



s 











0.1 

— 






— 




— 


'7.6" 

^ 









U) L2 1.4 1.6 18 2.0 2,2 2.4 

400r 


300 


200 


100 


— 1 — ^ — 

30-40 KC 















HYO 

R0PH< 
OM ^ 

3NE 

«SE 

8J”-. 



\ 

\ 








FR 





N. 













'A 




— 



















✓ 

✓ 

J 

*’/ 




^.6' 

















— 

— 




— - 












1.0 1.2 1,4 1.6 1.8 2.0 2Z 2.4 


Z 200r 
O T 


KX) 


12 

I 


"n 1 

40-50 KC 
















1.0 1.2 1.4 U6 1.8 2j0 2.2 2.4 


0 ) 

o 100 


‘ 0 
300 

200 

100 


1 

5( 

!)-60 































HYDROPHONE 

11.2"- 





a t*' 






FROM NOSE 






o«i 










;6" 

i 





O 

1.2 

1.4 

1.6 

IP 

2.0 

22 

2. 


6 

)-60 

( KC 































HYDROPHONE 
FROM NOSE 

11.2^ 


— ' 












•'8.1 












'7,6' 






















1.0 1.2 1.4 1.6 1.8 2P 2.2 2.4 


300 


200 


100 


1 1 1 

80-100 KC 





















y 

i 


— 












( 






HI 

roRO 

■ROM 

PHON 

NOS 

IE 8.1 
IE 

l" 




r.6" 






F 



^ II. 

2" 




















1.0 1.2 


1.6 1,8 
Pl-P. 


2P 22 2.4 


K * 


Figure 22. Effect of relative position of hydrophone 
and noise source on measured frequency distribution. 
V = 41 feet per second. 




MEASUREMENTS OF NOISE 


169 


accuracy of the sound versus K curves shown in Fig- 
ures 12 to 16, which were obtained with the hydro- 
phone in a fixed position. With the growth of the 
cavitation zone beyond the stage giving the maximum 
noise, the level measured by the fixed hydrophone is 
slightly low. This effect is small, however, being less 
than 2 db for the hemisphere nose at = 0.56 or the 
truncated hemisphere at = 1.51. Consequently, it 
does not alter the peculiar characteristics of the 
measurements shown, nor change the conclusions 
already presented. 

It is interesting to note that in Figures 18 to 20 the 
sound-pressure location curves for the hemisphere 
nose and tail rudder show more gradual reductions in 
noise on the side of the maximum which was toward 
the body of the model. This asymmetry became more 
pronounced at lower K values, while at high K’s, as 
obtained with the cut hemisphere nose in Figure 19, 
no definite asymmetry is observed. Examination of 
the photographs in each figure shows that at the 
lowest i^’s, cavitation is occurring at the junction 
between the streamlined strut which supports the 
projectile and the cylindrical projectile body. It is 
thought that this secondary cavitation is contribut- 
ing to the measured sound and is responsible for the 
asymmetry observed. 

7.4 3 Frequency Distribution 

of Cavitation Noise 

One of the objectives of this investigation was to 
measure the distribution of the high-frequency noise 
when cavitation occurs. Obtaining significant meas- 
urements of this type is very difficult, since the hy- 
drophone is separated from the sound source by 
water and the Lucite tunnel window, and since the 
geometry of the installation may cause reflection 
patterns that will bias the determinations. Even the 
use of focusing reflectors does not eliminate this 
possibility because even though the directivity may 
be good,^ standing waves may still bias the results. 
In addition, field calibrations have shown that the 
response of the reflectors themselves is not uniform 
over the frequency range of interest. As a result the 
relative position of the hydrophone and the sound 
source has an important influence, and a single set of 
measurements for one installation cannot be relied 
upon to indicate accurately either the magnitude or 
the distribution of the actual noise generated in the 
working section. This handicap was not present for 
the measurements that have been discussed in the 


previous sections because the main interest lay in the 
relative amount of noise obtained over a wide fre- 
quency band with and without cavitation. Neither 
the absolute magnitudes of the measured intensities 
nor the distribution within the band covered was of 
particular significance there. 

Because of the above considerations a series of 
experiments were made in which the relative position 
of a cavitating nose and the hydrophone was varied 
using the simple arrangement of the hydrophone in- 
serted in a Lucite blister clamped to the face of the 
working-section window. The noise level was recorded 
in each of several bands within the 20- to 100-kilo- 



Figure 23. Noise in 20- to 100-kc band by measurement 
and by rms summation from narrower bands. 


cycle range as well as for the entire range. The results 
of these measurements are shown in Figures 21, 22, 
and 23. Figure 21 gives the distribution measured on 
the truncated hemisphere nose at a velocity of 50 fps 
with the hydrophone located 11.2 in. downstream 
from the cavitating nose of a projectile (2-in. diam- 
eter model in 14-in. diameter working section). The 
measured levels in the various frequency bands are 
not uniform, the most predominant sound pressures 
being obtained in the 30- to 40-kilocycle band. Figure 
22 shows comparisons of the noise measured at 41 fps 
in each band and for the hydrophone at 11.2, 8.1, and 
7.6 in. aft of the model nose. For any band of fre- 
quencies although the location of the peak pressure 
and the shapes of the curves are similar for all hydro- 
phone positions, there are changes in the magnitude 
of the sound in some bands. This is definite indication 
of existence of some complex standing wave pattern 
caused by reflections from the tunnel walls. As cavi- 






170 


CAVITATION NOISE FROM UNDERWATER PROJECTILES 


tation grows and the falling noise level approaches 
the background level, the curves tend to converge, 
giving a more nearly uniform response over the en- 
tire frequency range independent of hydrophone po- 
sition. Such differences as do occur are most notice- 
able in the 30- to 40-kilocycle band. Note that all of 
these measurements were made at velocities and 
hydraulic pressures corresponding to K values at 
which there was no liberation of air from the main 
flow to cause attenuation of the noise. 


An interesting comparison is shown in Figure 23 by 
the two curves for the noise in the entire 20- to 100- 
kilocycle range. One was obtained by plotting the 
observed points, the other by plotting the square 
root of the sum of the squares of the sound pressures 
observed in individual bands. Aside from differences 
of about 10 per cent at the higher K range, which can 
be accounted for by filter cutoff characteristics, the 
agreement is very good. 


Chapter 8 

FORCES ON FINLESS BODY SHAPES 


81 INTRODUCTION 

T he hydrodynamic forces acting on the finless 
bodies of fin-stabilized projectiles are of interest 
to the designer because a knowledge of the magnitude 
and distribution of these forces forms a basis for 
understanding the overall forces acting on the com- 
plete projectile and, as is shown in Chapter 11, aids 
in clarifying the relationship between the lift, mo- 
ment, damping force, and damping moment. The 
effect of the body shape on the drag is discussed in 
Chapter 10. This chapter will be devoted to a discus- 
sion of the lift and moment and the relationship 
between them. 


8 2 DISTRIBUTED FORCES 

AND RESULTANT FORCES 

The structural designer of the shell of a projectile 
or an airship needs information on the distribution of 
forces over the surface of the body. On the other 
hand, in dealing with the external ballistics of the 
body shape it is usually sufficient to know the 
resultant of these distributed forces. For example, in 
the case of a well-streamlined body of revolution the 
dynamic pressure acting on the nose (parallel to the 
direction of motion) is nearly balanced by the dy- 
namic pressure on the afterbody, and the two taken 
together contribute but little to the total drag of the 
body. To determine the overall drag, which consists 
of the pressure drag (or form drag) plus skin friction 
drag, it is not necessary, therefore, to know the mag- 
nitude of the nose pressure or the afterbody pres- 
sure. However, to the structural designer these pres- 
sures may be important since the body structure 
must transmit them from one end of the body to the 
other. 

In the design of frail structures such as airship 
hulls, the distributed forces are of major importance. 
In the case of projectiles such as bombs, rockets, and 
torpedoes, the shells are usually made strong enough, 
because of other considerations, to withstand the 
hydrodynamic pressures encountered in a normal 
run. Therefore, we are usually interested only in the 
resultant forces and moments such as are measured 


in the wind tunnel or water tunnel. However, a bet- 
ter understanding of the behavior of the resultant 
forces may be gained by studying their origin in the 
distributed forces. 

The distributed forces acting on a body moving 
through a fluid medium may be divided into two 
groups: normal pressures acting at right angles to 
the surface and shear forces acting parallel to the 
surface. The shear forces contribute mainly to the 
drag, while the normal forces may contribute to the 
drag but are more important in determining the mo- 
ment and lift or cross force. In the following discus- 
sion we will, therefore, deal mainly with the normal 
pressures. 


8 8 STREAMLINED SHAPE 

IN A FRICTIONLESS FLUID 

For the purpose of this discussion it is convenient 
to start with the forces acting on a streamlined shape 
moving through an ideal frictionless fluid. Such a 
fluid does not exist since all real fluids are viscous to 
some extent. The force distribution with a friction- 
less fluid, therefore, cannot be measured but may be 
calculated from potential flow theory. The actual 
forces acting on the forepart of a well-streamlined 
shape moving at high Reynolds numbers through a 
real fluid are almost identical with those calculated 
for the ideal fluid. 

In Figure 1 is shown a streamlined body of revolu- 
tion moving rectilinearly with velocity v and angle of 
attack a. The solid line curve shows the transverse 
force distribution calculated for such motion through 
a frictionless fluid.^*^ The ordinate at each point along 
the axis gives the resultant force obtained by inte- 
grating the vertical component of the pressures ach 
ing on the surface of the body per unit of axial length 
at that station. It is seen that the forces on the fore- 
body are directed upward and on the afterbody 
downward, giving rise to a large upsetting moment, 
i.e., a moment which tends to increase the angle of 
attack a. Since the areas enclosed by the curve above 
and below the axis are equal, it is evident that this 
force distribution results in zero transverse force or 
lift but produces a pure couple only. 


172 


FORCES ON FINLESS BODY SHAPES 


« * STREAMLINED SHAPE 

IN A REAL FLUID 

In Figure 1 is also shown the force distribution 
calculated from pressure-distribution measurements 
made on the same body, which is a model of the air- 
ship RlOl. These data^ are shown by the circled 
points and dotted curve. It is seen that, on the fore- 
body, the measured forces are in very good agreement 
with the calculated values. On the afterbody the 
values measured with a real fluid are less than those 
calculated for the ideal fluid. It is known that this 
difference is due to the fact that, with a real viscous 
fluid, separation and vortex formation which occur 



Figure 1. Calculated and measured transverse force 
distribution. 


near the tail alter the force distribution on the 
afterbody .2^ 

This force distribution, unlike that of the ideal 
fluid, does give rise to a resultant lift, since in this 
case the downward force on the afterbody is not as 
large as the upward force on the forebody. The result- 
ant lift is equal to the difference between the areas 
enclosed by the experimental curve above and below 
the axis; or, equal to the area enclosed between the 
solid and dotted curves on the afterbody. 

In addition to the lift, the body is also subject to 
an upsetting moment. However, in the case of the 
real fluid this upsetting moment is not as large as 
with the ideal fluid because the force on the afterbody 
is smaller. Nevertheless, a comparison of the areas 
under the curves of Figure 1 shows that the magni- 
tude of the moment is still large in comparison with 


the resultant lift. That is, the moment is due to real 
forces acting directly on the body which are con- 
siderably larger than the resultant lift. 


* 5 RESOLUTION OF FORCES 

In dealing with the external ballistics of projectiles 
we are usually interested only in the resultant forces 
and moments, since the motion of the body as a 
whole is determined by them. These resultants are 
easily determined by direct measurement in water or 



wind tunnel or towing tank. The determination of 
the force distribution, on the other hand, requires 
laborious processes involving integration from pres- 
sure-distribution measurements and evaluation of the 
skin friction drag. 

Direct force measurements give the magnitudes of 
the moment and of the lift, but not the force distribu- 
tion. To establish a relationship between the moment 
and the lift, it is usually assumed that the moment is 
a direct result of the lift force acting at some point 


EVALUATION OF THE THEORETICAL MOMENT 


173 


called the center of pressure CP. To determine the 
location of CP with reference to the center of gravity 
CG, we divide the moment M about CG by the lift 
force L, this ratio giving the lever arm Icp, i.e., 

Icp = - X' 

This conventional method of resolution leads to some 
incongruities. For instance, in the case shown in Fig- 
ure 1, the moment tends to turn the body clockwise 
and the lift acts upward. If the moment is attributed 
to the lift, then the lift must be acting at some point 
ahead of CG. Also, since in this case the lift is small 
and the moment is large, Icp comes out so large that 
the lift appears to act 0.8-body-length ahead of the 
nose. Obviously, a transverse force cannot be trans- 
mitted to the body through the water from a point 
ahead of the body. Furthermore, if we were to modify 
the body shape so as to increase the lift, for instance 
by making the tail more blunt or by adding fins, we 
would thereby decrease the moment. Again we arrive 
at an incongruity, i.e., the moment, which supposedly 
is due to the lift, diminishes as the lift grows. With 
the oversimplified relationship embodied in equa- 
tion (1), this is explained by saying that Icp becomes 
smaller or even changes sign, i.e., the center of pres- 
sure is moving aft along the body axis. 

The forces may be resolved in a different manner 
which gives a clearer and more consistent picture of 
the true conditions. Instead of taking, for the case of 
the real fluid, the force distribution shown by the ex- 
perimental curve in Figure 1, we may say that there 
are two sets of forces acting on the body, as shown in 
Figure 2. One (shown at A) is the same as the calcu- 
lated force distribution of Figure 1, which results in a 
pure couple and zero lift. The other distributed force 
is as shown in Figure 2B, equal to the difference be- 
tween the calculated and experimental curves of Fig- 
ure 1. The area under this curve represents the lift 
force. It is seen that the moment about CG of this lift 
is of opposite sense to, and partially balances, the 
moment due to the force distribution shown at A. 
The resultant moment acting on the body in a real 
fluid is then equal to the difference between the up- 
setting moment of the ideal fluid and the righting 
moment of the actual lift force. 

The several inconsistencies which were seen to arise 
from the conventional force resolution are now elimi- 
nated. All forces now act directly on the body. The 
lift force is seen to act on that part of the body where 
the physical phenomena (separation and vortex for- 


mation) which give rise to it actually occur. The fact 
that as the lift force grows the resultant moment 
tends toward greater stability is also consistent. Any 
tail surfaces that may be added would contribute an 
additional lift increment acting approximately at the 
same location and in the same direction as the hull 
lift. 

« « EVALUATION OF THE 

THEORETICAL MOMENT 

To determine the line of action of the lift force by 
the method outlined above, it is not necessary to 



Figure 3. Inertia coefficients of an ellipsoid moving in 
a fluid, Ki, axial; K 2 , transverse; A', rotation. 


know the theoretical and actual force distributions 
over the entire body. Only the resultant magnitudes 
of the theoretical moment and the actual moment 
and lift are required. The righting moment of the lift 
is equal to the difference between the theoretical and 
actual moments. The ratio of this righting moment to 
the lift force gives the distance from CG to the line of 
action of the lift. 

The resultant theoretical moment for a stream- 
lined body of revolution without fins may be de- 
termined with sufficient accuracy for most practical 
needs by a simple calculation sometimes used in air- 
ship work. This is based on the assumption that the 
theoretical moment for a well-streamlined shape is 


174 


FORCES ON FINLESS BODY SHAPES 


equal to that of an ellipsoid of revolution having the 
same volume and length. For an ellipsoid, the the- 
oretical hull moment H is given 

H = y 2 pv\k 2 - ki)V sin 2a (2) 

where ki and k 2 are the coefficients of apparent mass 
of ellipsoids of revolution for longitudinal and trans- 


verse motion, respectively, as calculated by Lamb,^^ 
and V is the volume of the projectile. The only possi- 
ble source of inaccuracy involved is in the selection of 
the equivalent ellipsoid. This error, however, is very 
small for projectiles of slenderness ratio (l/d) of 7 or 
more, since, as may be seen in Figure 3, the values of 
ki and k 2 change but slightly in this range. 



Chapter 9 

STABILIZING SURFACES ON NONROTATING PROJECTILES 


8 1 PURPOSE OF STABILIZING SURFACES 

A symmetrical projectile, supported at its center 
of gravity and situated in a completely uniform 
flow, should be in a position of equilibrium and the 
moment coefficient Cm should be zero. If this pro- 
jectile position be altered slightly and the projectile 
itself be free to move under the new distribution of 
forces, it is said to be statically stable when it tends to 
return to the equilibrium position; statically un- 
stable, when it tends to move farther away; neutral 
when it remains in the new position. In the first case, 
the resultant of all the pressures will act as though it 
were being applied aft of the center of gravity; in the 
second, as though it were ahead. It is possible for this 
resultant to act as though it were being applied at 
such a distance forward of the center of gravity as to 
be in front of the nose. 

The purpose of a stabilizing surface is to provide a 
desired degree of static stability in a projectile which 
would be inherently unstable without it. It does this 
by creating a cross force some distance aft of the 
center of gravity which produces the righting mo- 
ment. The cross force arises because the stabilizing 
surfaces will deflect some of the surrounding fluid 
when the projectile yaws or pitches. Stabilizing sur- 
faces also provide additional damping forces and, 
hence, damping moments to give dynamic as well as 
static stability. 

8 2 FORM AND ACTION 

OF STABILIZING SURFACES 

Stabilizing surfaces are usually fins, rings, or box 
tails. Fins are essentially flat surfaces set in planes 
which contain the longitudinal axis of the projectile. 
Ring or box tails are made with all surface elements 
parallel either to the projectile axis or to the normal 
local flow direction. The stabilizing surfaces may be 
attached directly to the body or afterbody or to 
booms extending back from the body proper. The fin 
span, the ring diameter, or the diagonal length of box 
fins must not exceed the body diameter of any pro- 
jectile launched from tubes or gun barrels but may be 
greater when launched by other means. A special 
case is the collapsible fin tail for which the fins are 


folded initially to permit tube launching, unfolding 
thereafter to give a much larger span with greater 
effectiveness. Most stabilizing surfaces are immova- 
ble. However, certain projectiles, such as torpedoes, 
are equipped with movable rudders in addition to 
fixed fins and rings and hence, through the action of 
suitable control engines, can be steered in any desired 
direction. 

Fundamentally, the magnitude of the cross force 
developed by a stabilizing surface depends upon the 
lateral momentum imparted to the fluid. The force is 
proportional to the amount of fluid deflected and the 
magnitude of the deflection as measured by the simul- 
taneous change in the velocity vector. Thus, a given 
force can be obtained by deflecting a small amount of 
fluid through a large angle or by deflecting a greater 
amount through a smaller angle. These effects, which 
have been discussed qualitatively, with the aid of 
flow diagrams, in Chapter 3, are the basis for geo- 
metric differences in tail designs. Actually, the drag 
of stabilizing surfaces also contributes to the stabilizing 
moment. However, in general, the drag coefficient is 
held to a low value since a large drag coefficient is 
undesirable in all but very low-velocity projectiles. 

8 3 EFFECT OF DESIGN VARIABLES 

Standard types of tails— fin, ring, and box — have 
been mentioned above. Additional design variables 
are the fin span which is the dimension equivalent to 
ring diameter and box diagonal ; the fin, ring, or box 
length which is measured in a direction parallel to the 
projectile longitudinal axis; boom locations for stabi- 
lizing surfaces as opposed to location on the body or 
afterbody; and the overall length of the projectile it- 
self. Specific projectiles will be discussed later in some 
detail, but the main conclusions as to the effects of 
these design variables are presented now. 

Conclusions 

1. The ring tail is far more effective in producing 
stability than the fin type when physical dimensions 
only are considered. 

2. An increase in the outside diameter (or span) of 
either the ring or fin tail causes a very marked in- 


175 


176 


STABILIZING SURFACES ON NONROTATING PROJECTILES 


crease in the stabilizing moment because of the larger 
quantity of fluid affected and the lessening relative 
effect of body interference and tip losses. 

3. An increase in the (axial) length of fins beyond 
about two-thirds of the fin (diametrical) span pro- 
duces very little, if any, increase in stability. 

4. The critical length of a ring, beyond which little 
increase in stability occurs, lies between one-half and 
two-thirds of the ring diameter. 

5. Stabilizing surfaces separated from the main 
body by a boom cause increased moments because of 



Figure 1. Moment coefficient versus fin length and 
diameter. Fin tails. 


the increased lever arm to the center of gravity and 
because body influence of the flow at the tail surfaces 
is reduced. 

6. Varying the overall length of a given projectile 
from 7 to 14 calibers (by adding to the cylindrical 
body section and keeping the percentage distance of 
the center of gravity from the nose a constant) gave, 
for the same fin or ring tail, a restoring moment di- 
rectly proportional to the overall length. In other 
words, the moment coefficient was constant. This 
means that the contribution of the tail surfaces to the 
restoring moment is also proportional to the pro- 
jectile length or that the actual forces on the tail 
surfaces are independent of the length. 


Fixed Fin Tails 

The manner in which the moment coefficient Cm 
is affected by changes in fin proportions is well il- 
lustrated by tests on the 5-inch HVAR rocket.^® Fig- 
ure 1 shows how the moment coefficient changes with 
varying length and span of the fin. This curve sheet 
covers fins with spans up to 4 calibers and lengths 
increasing (from the after end forward) up to 3.2 
calibers. It may be seen that an increase in fin length 
produces relatively little increase in the moment co- 
efficient after a length of about two-thirds of the span 
dimension has been reached. Additional length does 
not increase the effectiveness of the fin in deflecting 
the fluid but results in nearly the same angular de- 
flection and, hence, the same cross force. The center 
of pressure on the fins moves forward as the tail is 
lengthened. This decreases the lever arm of the 
stabilizing cross force and tends to reduce the mo- 
ment coefficient Cm. For fin lengths below two-thirds 



Figure 2. Sixty-millimeter mortar projectile. 

the span, this decrease in lever arm is, relatively, 
much smaller than the increase in cross force due to 
the lengthening. For excessively long fins, the reverse 
is true. 

It may also be seen from these curves that as the 
span of a given length fin tail is increased, the gain 
in moiAent coefficient is greater than the change in 
fin area. Furthermore, the gain is more pronounced 
for a unit increase when the span is short. Apparently 
a unit fin area near the body surface is affected by 
body interference and the tip losses are relatively 
higher. 

The influence of body interference on the effective- 
ness of fin tails is shown by the performance of a tail 
having the same outside diameter as the projectile 
body. The example chosen is the 60-mm mortar pro- 
jectile^^ with a tail of eight fins attached directly to 
the tapering afterbody as shown in Figure 2. In order 
to increase the stability, tests were made with the tail 
mounted on booms of different lengths. The increases 
obtained are shown by the force coefficient curves in 
Figure 3. A curve is also included showing the per 


EFFECT OF DESIGN VARIABLES 


177 






0 aa 0.4 as as i.o 12 


BOOM LENGTH, CALIBERS 


Figure 3. Moment and force coefficients. Sixty-millimeter mortar projectile. 


cent increase in stabilizing moment coefficient plotted 
against boom length in calibers for a yaw angle of 4 
degrees. Note that Cm increases at first at a rate 
greater than the linear change that would be due to 
increasing the boom length alone. The extra effect 
is due to the fact that better flow conditions are ob- 
tained over the fins because of the increasing distance 
from the afterbody. The very large magnitude of the 
percentage increase in Cm with increasing boom 
length is due, in this case, to the fact that the boom 
makes up a relatively large percentage of the overall 
length. 

" ' ' Ring Tails 

Typical effects from varying the length and di- 
ameter of ring tails are shown by the performance of 


a group of tails having a diameter larger than the 
body of the projectile. Figure 4 shows the moment 
coefficient for the 5-in. HVAR projectile with a series 
of ring tails having diameters of 1.5 to 2.5 calibers, 
and lengths varying from 0.25 to 2.5 calibers. These 
curves show only a slight change in moment for any 
increase in ring length beyond one-half to two-thirds 
of the ring diameter. 

The data in these curves also illustrate a rapid in- 
crease in moment coefficient with ring diameter simi- 
lar to that shown for increasing the span of plain fin 
tails. 

The performance of ring tails having the same di- 
ameter as the projectile body is similar to that of fin 
tails no larger than the body diameter. Because 
changes in ring length show relatively small effects, 
the most satisfactory way to increase stability in this 


178 


STABILIZING SURFACES ON NONROTATING PROJECTILES 


case is by means of a boom, as for fin tails. Many tests 
made to determine the suitability of the ring tail for 
the 4.5-in. rocket^^-^® illustrate this point. Figure 5 
is a photograph of the model of the 4.5-in. rocket with 
a ring tail and boom. Figure 6 shows the correspond- 
ing performance curves and curves giving the per 
cent increase in moment coefficient due to the boom. 
As was observed for the fin tail on the 60-mm mortar 
projectile, the increase is greater than can be ac- 
counted for by the increase in lever arm due to the 

LENGTH OF RING, CAUSERS 



Figure 4. Moment coefficients versus ring dimen- 
sions; 5-in. HVAR ring tails. 


added length, indicating that the tail is more effective 
in producing cross force with the longer boom. The 
increase in Cm with boom length is very much less 
than was the case with the 60-mm mortar projectile, 
this, of course, being due to the fact that the 4.5-in. 
rocket is a long projectile and the boom length is 
relatively small in comparison. 

The 7.2-in. chemical rocket,^^ shown in Figure 7, is, 
in effect, a projectile with a ring tail of the same di- 
ameter as the body mounted on a boom 0.43 caliber 
in diameter and 3.87 calibers long. This will serve to 
illustrate the effect on stability of a boom of great 
length. The moment coefficient for the rocket with 


the standard ring tail (No. 61 in Figure 7) is approxi- 
mately 0.056 at 3 degrees yaw. This is a much 
greater moment coefficient than is usually found 
when the ring diameter does not exceed that of the 
body. The addition of fins to this projectile resulted 
in a considerable increase in the stabilizing moment. 
The fins were 1.39 calibers in diameter and 1.18 cali- 
bers in length, shown as tail No. 62 in Figure 7. Inas- 
much as these fins project beyond the ring, the in- 
crease in moment coefficient is not unexpected. The 
curves in Figure 8 indicate how the stability is 
affected by the addition of fins, and it is seen that the 
moment coefficient is increased approximately 50 per 
cent. 

An illustration of the effect of body shape on fin 
effectiveness is given by tests to determine the 
feasibility of applying a ring tail to the Mark 13 
torpedo.^® These rings were of the same diameter as 
the torpedo body and were mounted on fins attached 
to the tapered afterbody. Figure 9 gives the moment 
coefficient for the torpedo with three types of ring 



Figure 5. Four and one-half-inch rocket with ring 
tail and boom. 


tails; a cylindrical ring, a ring with a 16-degree in- 
cluded cone angle, and one with an 8-degree included 
cone angle. The 8-degree ring conforms to the angle 
of flow as determined by studies in the polarized light 
flume. The resulting flow line drawing is shown in 
Figure 10.^ The 16-degree cone angle causes a con- 
verging flow through the ring, and the cylindrical 
section causes a diverging flow through the ring as 
compared to the normal flow without the ring. 

In the diagrams of Figure 9, the positive moment 
coefficients denote a destabilizing static moment, and 
the negative coefficients stable moments. An exami- 
nation of the curves discloses that with one exception 
the addition of the ring gives an additional righting 
force. With the 16-degree conical ring the effective- 
ness of the tail surfaces is actually reduced if the 
ring width is large. In general, the stabilizing effect 
of the ring increases with decreasing cone angle, so 
that the greatest stabilizing effect is obtained with 
the cylindrical ring. This is due to both large cross 


a A complete description of the determination of flow angles 
over this afterbody is given in Chapter 3. 


feM'ii)K\'n\rj 


EFFECT OF DESIGN VARIABLES 


179 



YAW ANGLE, DEGREES 




Figure 6. Moment and force coefficients; 4.5-in. rocket with ring tail and boom. 



fins. 



Figure 8. Moment coefficients. Chemical rocket (7.2- 
in.). 


OTIVUDKNTI 



180 


STABILIZING SURFACES ON NONROTATING PROJECTILES 



0 2 4 6 8 10 12 

PITCH ANGLE, DEGREES 




II ^ I ■ 

0 2 4 6 8 10 12 

PITCH fiHGLE, DEGREES 


16* CONICAL RINGS 
(CONVERGING FLO^ 


8* CONICAL RINGS CYLINDRICAL RINGS 

(RING PARALLEL TO FLO\^ (DIVERGING FLOW) 


NOTE: FOR DllyENSIONS IN CAUSERS, DIVIDE DIMENSIONS ON CURVES BY 2 


Figure 9, Moment coefficients. Mk 13 torpedo with ring tails. 





Figure 10. Flow line drawing. Eight-degree ring tail 

on the Mk 13 torpedo. Figure 11. High-drag ring tails. 


^t ^kiDKyn ) 


I— 18 . 8 ' 


EFFECT OF DESIGN VARIABLES 


181 


force and high drag. As shown in Chapter 3, when the 
projectile is yawed, the mndward ring surface of this 
tail will act at a larger angle of attack and will cause 
more lateral deflection of the fluid it contacts than 
does the leeward surface. However, even at zero yaw 
the ring does not match the flow and the drag is high ; 
consequently, this is not the normal method of ob- 
taining a large cross force and moment. The effect of 
the cylindrical ring increases with length. Apparenth' 
it was not carried to the point of diminishing returns 
obtained in the tests with the 5-in. HVAR rocket. It 
should be noted that the stability of the cylindrical 
ring as shown is not typical of actual torpedoes since 
with adjustable rudders complete static stabilit}^ is 
not necessarily desirable. 

^ ^ * High-Drag Ring Tails 

A special adaption of the ring tail to produce high 
drag is of interest. Here the tail was intended to limit 
the terminal velocity of a bomb to prevent deep 
penetration on impact, and at the same time supply 
sufficient moment for good stability. Figure 1 1 shows 
a straight ring tail, a conical ring set approximate!}^ 
to the flow lines, and two conical rings expanding in 
the aft direction. As shown by the coefficient curves 
of Figure 12, the cylindrical and normally tapered 
rings have about the same drag, the value being 
approximately what would be expected for this type 
of tail. However, when the taper of the ring is re- 
versed, as in models C and E, the drag is increased 
about 2}/2 times. Tail E is the same as tail C except 
that it is installed on a short boom. As in the case of 
the results obtained with the Mark 13 torpedo, the 
greatest cross force is given by the designs that cause 
the most deflection of the fluid, tails A, C, and E. Of 
these, tail E is most effective because interference 
from the body is reduced. It is better than tail A 
which is also on a boom, because it is more effective 
in deflecting the surrounding fluid. Tail B, with the 
cone angle aligned approximately to the normal flow, 
presents the least obstruction and, with yaw, causes 
the least lateral deflection. The resultant moment 
coefficients are roughly in agreement with the cross 
force trends. 


9.3.5 Effect of Body Length 

One remarkable effect noticed in connection with 
the investigation of ring tails is that the moment 
coefficient for a given tail is practically constant for 



















m 

-^1 

DOEL 

L 

E 

— 

— 





























































B 





)DEL 

A 












































0 



Figure 12. Moment and force coefficients. High-drag 
ring tails. 




182 


STABILIZING SURFACES ON NONROTATING PROJECTILES 


overall projectile lengths between 7 and 14 calibers. 
This refers to bullet-shaped projectiles, with the di- 
ameter of the ring tail greater than the body diam- 
eter, and for which the center of gravity is assumed 
at a fixed per cent of the overall length from the nose 
tip. 

Figure 13 gives the moment coefficient versus over- 
all length of projectile for ten ring tails of various 


OVER -ALL LENGTH IN CAUSERS 


0 




9, 

7-2^ 



IJ5 ( 

^LIB 

ER i 

31AM ' 

RINC 


=t- 

-ai 


97- 

y- 


97-^ 
























> • 








Uo 

CAUBER 

DIAI 

* RING 


> 













•0 

f-a2 



5:27 












> ^ 










— 





> -(X3 








25 

96-3-' 

CAUBER 

DIM 

A Rf 

4G 






1 


H 




1 

96- 
1 

1 





|-0.4 




r 

i 

H 

1 

TA 

IL N 

OL 96 

A 







t 

! 

i 










-05 





L_ 




YAV 

i A^ 

1 i 

I 6 LE 

1 

.3* 

1 




Figure 13. Moment coefficients versus projectile 
length; 5-in. HVAR ring tails. 


lengths and diameters. It is seen that all but two 
of the curves show a practically constant value for 
the moment coefficient. The abnormal performance 
of the two tails for body lengths between 7 and 10 
calibers has not been investigated. 

Tests of finless body shapes (see Chapter 8) have 
shown, in the few instances where only the length was 
varied, that the moment coefficient for the body alone 
increases very slightly for yaw angles of 3 degrees or 
less, even with large increases in length, if the 


shortest projectile is not less than 4 calibers long. 
Thus it can be concluded that the forces on the 
tail surfaces in Figure 13 remained sensibly un- 
changed throughout. This conclusion is logical since 
the body shape ahead of the tail remains fixed as the 




Figure 14. Four and one-half-inch rocket with orig- 
inal collapsible fin tail. 

length is increased so that the flow into the tail prob- 
ably is also unaffected. As already seen in the case 
of the 4.5-in. rocket, this result is not obtained if the 
length is changed by boom additions so that body 
interference is reduced. 

Fin tails on this same projectile also show a tend- 
ency toward a constant value of coefficient with 





Figure 15. Rocket (2.36-in.) with original fixed fin 
tail. 


varying body length, but the effect is not so pro- 
nounced as with ring tails. For a given yaw angle and 
a given tail the moment coefficient is quite constant 
for body lengths between 10 and 14 calibers. As the 
length changes from 10 to 7 calibers, the moment 



Figure 16. Rocket (2.36-in.) with No. 2 collapsible fin Figure 17. Rocket (2.36-in.) with No. 5 collapsible fin 

tail. tail. 


jj OM IDFN Tl \l. ) 



EFFECT OF DESIGN VARIABLES 


183 




YAW ANGLE. DEGREES 

Figure 18. Moment and force coefficients. 2.36-in. rocket. 


coefficient will decrease between 5 and 20 per cent quence, a considerable increase in the stabilizing 
depending on the yaw angle and tail design. moment would be expected. Figure 18 shows curves 

of the force coefficients for this rocket equipped with 


® ^ ® Collapsible Fins 

Many designs of collapsible fin tails for rockets 
have been made as these have some advantages over 
other types. The collapsible design allows the use 
of as great a fin span as desired and still permits the 
launching of the rocket through a tube of the same 
diameter as the body. However, owing to the many 
moving parts of this type of tail, it is not, mechanic- 
ally, as desirable as a simple fin or ring form. 

Figure 14 is a photograph of the original collapsi- 
ble fin tail of the 4.5-in. rocket.^^-^® This tail gave a 
stabilizing moment considerably greater than other 
types of fin and ring tails that were designed for this 
projectile. The efficacy of this type of tail is in agree- 
ment with the general discussion on fin tails in that 
it takes advantage of a rather large span for the fins, 
which is very effective in producing both a cross 
force and a drag at the tail and, hence, a stabilizing 
moment. 

The most extensive and reliable data on collapsible 
fins are those relating to the 2.36-in. rocket.^^’^® 
This projectile was originally designed with long, 
parallel fixed fins having an outside diameter equal 
to the diameter of the body. Figure 15 is a photo- 
graph of the original design of this rocket. In order 
to increase the stability, several different tail designs 
were made and tested. Figures 16 and 17 show two of 
the designs which were given the laboratory designa- 
tions of tail No. 2 and tail No. 5. It is apparent that 
the span of the extended fins has been greatly 
increased over the original design and, as a conse- 




YAW ANGLE * 3* OVERALL LENGTH » BJB4 CALIBERS 

Figure 19. Fin and ring tails all having the same 
moment coefficient. 


ICOVFrDKM 


184 


STABILIZING SURFACES ON NONROTATING PROJECTILES 


the original fixed fins and also with the two types of 
collapsible fins. The collapsible fins have resulted in 
an increase of several hundred per cent in the stabiliz- 
ing moment. The moment for tail No. 5 is much 
greater than that for tail No. 2 because its outside 
diameter is 9.15 in., with only 7.25 in. for tail No. 2. 

It should be noted that a material increase in drag 
results from the use of the collapsible fin tail. Except 
for a very high drag, however, the drag effect on the 
stabilizing moment is usually not important. This 
can be shown as follows: 

The moment (about the center of gravity) acting 
on a projectile is given by the expression 

Mcg ~ Nel 

in which N = the sum of the components of the 
drag and cross force acting normal to 
projectile axis, or 

N — drag X sin + cross force X cos xf/, 
\{/ = yaw angle, 

I = length of projectile, 
e = center-of-pressure eccentricity ex- 
pressed as a percentage of 1. 


From the equation for N it is seen that for low values 
of drag and yaw angle, the term involving drag will 
be small compared to that involving the cross force 
and can, therefore, be omitted with only a small 
error. In other words, only comparatively large 
values of drag can be considered as affecting the 
moment. 

® ’ Ring versus Fin Tails 

It is instructive to compare the dimensions of 
various fin and ring tails that have been designed to 
give the same stabilizing moment coefficient. 

In Figure 19 are shown the proportions of three 
ring tails and three fin tails all giving a moment 
coefficient of 0.225 when applied to the 5-in. HVAR 
projectile. It is very apparent from Figure 19 how 
much the length of either fins or rings must be in- 
creased to counteract the effect of a decrease in fin 
span or ring diameter. Also the smaller physical 
dimensions of the ring tails in all cases show how 
much more effective the ring is than the fin in pro- 
ducing stability. 


yvtjnl.NTIAl. ) 


Chapter 10 

EFFECTS OF PROJECTILE COMPONENTS ON DRAG 
CROSS FORCE, AND LIFT 


101 INTRODUCTION 

T he use of stabilizing surfaces on nonrotating 
bodies and forces on finless body shapes were dis- 
cussed in Chapters 8 and 9. This chapter extends 
consideration to the effects of projectile components 
on drag, cross force, and lift. 


102 DEFINITIONS 

Drag D is the force in pounds exerted on the pro- 
jectile parallel with the direction of motion, that is, 
it is the resistance offered to relative motion between 
the projectile and the surrounding fluid. The drag is 
positive when acting in a direction opposite to the 
direction of motion. 

The cross force C is the force in pounds exerted on 
the projectile normal to the direction of motion and 
in a horizontal plane. A positive cross force acts to 
the right for an observer facing in the direction of 
travel. 

The lift L is the force in pounds exerted on the 
projectile normal to the direction of motion and in a 
vertical plane. It is positive when acting upward. 

It may be seen, by reference to Figure 1, that these 
forces act along the intersections of the horizontal 
and vertical planes through the longitudinal axis of 
the projectile and the plane perpendicular to these 
two through the center of pressure for zero yaw and 
pitch angles. 


10.2 FORMULAS 


II 

pv'^Ad 

L 2 J 

(1) 

C = Cc 

1 1 

b 

1 1 

(2) 

L = Cl 

Pv‘^Ad 

L 2 J 

(3) 



(4) 


V 


where D = drag force, in pounds; 


C = cross force, in pounds; 

L = lift force, in pounds; 
p = mass density of fluid in slugs per cubic 
foot; 

weight per cubic foot 


P = 


32.2 


1.94 for fresh 


water and 1.99 for sea water at 60 F; 

V = mean relative velocity between water 

and projectile in feet per second; 

Ad = area in square feet at the maximum cross 
section of projectile taken normal to its 
longitudinal axis; 

R = Reynolds number; 

I = overall length of projectile, in feet; 

V = kinematic viscosity of fluid in square 

feet per second (values from tables or 
graphs, about 1.057 X 10“^ sfs for fresh 
water at 70 F). 


10* DISCUSSION OF THE FORMULAS 


It may be seen that the bracket portion of the first 
three formulas is identical. The term {pv^/ 2) represents 
the kinetic energy of a unit volume of the fluid. For a 
given projectile in water of a given kind and tem- 
perature, this term will be a constant and the formu- 
las will become 


D = CdKv^ 

(5) 

C = CcKv^ 

(6) 

L = ClKv-^ 

(7) 


where K is the constant (pAd/2). 

The terms D,C, L, and v are measured directly in 
the water tunnel and from these values {K being 
known), the coefficients Cd, Cc, and Cl may be de- 
termined for Reynolds numbers corresponding to the 
velocities obtainable. The Reynolds number for the 
full-size projectile is generally very much higher than 
for a model. The problem then reduces to a determi- 
nation of the effect of projectile components on the 
coefficients as functions of Reynolds numbers. To 
estimate the effect on full-size bodies the results from 
tunnel measurements are extrapolated to full-scale 
Reynolds numbers. 


Wi'idT.miID 


185 


186 


EFFECTS OF PROJECTILE COMPONENTS 


105 DRAG 

The total drag D and the total drag coefficient Cd 
are, ordinarily, the only drag values measured or 
calculated. However, this total drag may be thought 
of as being composed of two parts, called the form 
drag and the skin friction drag. 

® ^ Form Drag 

The form drag arises from the pressures normal to 
a body and may be determined by integrating the 
components of the pressures parallel to the direction 
of motion. It is proportional to the velocity squared 
and to the projected area, for a given Reynolds 
number. The resistance of a flat plate normal to the 



flow is practically all form drag and is due to the 
difference in pressure on the two sides. 


® ^ Skin Friction Drag 

The skin friction drag arises from the shear stresses 
on the body surface and its value can be determined 
by integrating these stresses over the wetted surface 
of the projectile. This drag is caused by the viscosity 
of the fluid and therefore is a function of the viscosity 
as well as the velocity. It is usually expressed as a 
function of Reynolds number. A flat plate parallel 
to the flow is an example of a body with nearly pure 
skin friction drag. This skin friction drag is influenced 


by the type of flow which may be laminar or turbu- 
lent, or in a transition zone between. With laminar 
flow, the fluid layers slide smoothly over those nearer 
the body with relatively small friction or shear be- 
tween layers. Turbulence, strictly speaking, is a con- 
dition of irregular fluctuations, which is distinct 
from vortex motion in general, and which results in a 
continuous interchange of fluid between streamlines 
and hence, a relatively high friction between different 
layers of fluid. Therefore, under conditions of turbu- 
lent flow, the drag is higher than when the flow is 
laminar. Flow conditions are turbulent for full-scale 
projectiles and for nearly all models used in tests such 
as are described in this volume. A few highly stream- 
lined models have shown values of the drag coefficient 
which were in the transition zone between laminar 
and turbulent flow conditions. 


Skin Friction Coefficient 


The skin friction coefficient of a flat plate, for 
which sensibly all of the drag is due to the skin 
friction, is 


Cf 


2F 

pv^S 


( 8 ) 


where F = the frictional drag force, in pounds, and 
S = the area of the wetted surface, in square 
feet. 


Figure 2 is a logarithmic plot of this skin friction 
coefficient against Reynolds number for smooth 
plates for both laminar and turbulent flow condi- 
tions.^^ Three of the possible types of transition 
curves, between the laminar and turbulent flow, are 
also shown. 

Formula (8), above, cannot be used directly for 
projectile models and the method of calculation 
based on pressure distribution involves special con- 
struction and numerous measurements. Frequently, 
an approximate evaluation of the skin friction drag 
and form drag coefficients is all that is necessary and 
these may be readily calculated if we assume that the 
skin friction coefficient for the model is the same as 
that for a flat plate of the same length and area. If, to 
distinguish between them, we call the skin friction 
coefficient of the model Cdf and that of a flat plate 
Cf (as before), then the former, which is based on the 
cross-sectional area A d, is 


Cdf = 


2D 

PV^Ad^ 


( 9 ) 


DRAG 


187 



REYNOLDS NUMBER. R 

Figure 2. Effect of flow types and Reynolds number on the skin friction coefficient of a flat plate parallel to the flow. 


and the latter, based on total wetted surface is 
2F 
pv^S 

Cfpv^S 


Cf = 


or 


( 8 ) 


( 10 ) 


Substituting this value of F for Z), which it is now 
assumed to equal for drag due to the skin friction, 
gives 

Cdf = 4-Cf. (11) 


This provides the simple relation between the two 
objects, which says, in words, that the skin friction 
coefficient of the models is equal to the skin friction 
coefficient of the flat plate multiplied by the ratio of 
the total wetted area of the model to its maximum 
cross-sectional area (in a plane perpendicular to its 
longitudinal axis). These areas may be calculated 
from the model dimensions and the Cf values taken 
from Figure 2. The values obtained in this manner 
will be somewhat different from those which actually 
exist because the original assumption neglects the 
fact that, without separations, the fluid velocities 
over the greater portion of the surface of a body of 
revolution will be higher than those for a plate in the 
same original velocity flow due to the accelerations 
necessary in passing such an object. If separation 
does occur, the surface velocities are low and may 
even reverse direction so the contribution to skin 


friction is small. It is affected, in addition, by dif- 
ferences in the rate of growth of the boundary layer. 
These inaccuracies are usually small, and the formula 
provides a simple way to obtain generally satisfactory 
information on this factor. 

10 5.4 Form Drag Coefficient 

The form drag coefficient can now be evaluated as 
the difference between the total drag coefficient and 
the skin friction drag coefficient at the same Reynolds 
number. Of course, when the skin friction drag co- 
efficient is obtained in the manner described, the form 
drag coefficient values will be governed by the same 
assumption. 

No instance is at hand when there has been an in- 
crease in the form drag coefficient with increased 
velocity of water flow. The value could remain con- 
stant with increased Reynolds number only if the 
flow pattern remained the same, so that pressures 
normal to the surface, expressed as fractions of the 
dynamic pressure, remained unchanged. Thus, the 
normal tendency will be for the form drag coefficient 
to be reduced by higher velocities as any existing 
separations in the flow will be reduced in extent at 
higher Reynolds numbers. 

10.5.5 Drag in Relation to Flow 

Usually a low drag is desired and this is obtained 


( tom ll>IM I \l ') 


188 


EFFECTS OF PROJECTILE COMPONENTS 


through “streamlining/’^ that is, by having a shape 
primarily with minimum form drag. The essential 
point is that drag is intimately related to the nature 
of the flow produced and that this flow results from 
the entire body shape, starting with the nose. Thus, 
it would be practically meaningless to say that a 
certain tail had 10 per cent less drag than another 
unless the conditions of flow about the projectile 
ahead of the tail were known. This might be true for 
a certain Reynolds number and a model with a 
streamlined nose, yet it is possible that there would 
be no differences in the measured drag of these tails 
at the same R value if a blunt nose were used. As an 
illustration of the importance of flow character, we 
may consider the AN-Mark 41 bomb (see Chapter 
16). The prototype tested had a very blunt nose and 
several lugs and other protrusions from the cylin- 
drical body. When all these protrusions were removed 
and the drag was measured, no change was recorded. 
The very blunt nose caused the high-velocity water 
to separate at the junction between the nose and 
cylindrical body and form an envelope of relatively 
stagnant water. Since this enclosed the protrusions, 
they had no measurable influence on the drag under 
these flow conditions. When a less blunt nose was 
used, the flow clung more closely to the body, high- 
velocity water did strike the protrusions and the 
difference in the drag with this nose for the body with 
and without protrusions was more than 10 per cent 
at the same R value. 

® ® Nose Influence 

Since the flow pattern starts to form at the nose, 
we may begin to discuss the nose effect by consider- 
ing a circular plate perpendicular to the flow, since 
such an object is, in a loose sense, all nose. Somewhat 
more accurately, it is an object with a blunt nose and 
blunt afterbody but no body. It has been found to 
have a drag coefficient of 1.12 over a wide range of R 
values.®"" If now we give this plate a length, convert- 
ing it to a cylindrical body with sharply blunt nose 
and afterbody, the drag coefficient will first diminish 
b}^ about 25 per cent when the length is three times 
the diameter and then gradually increase again with 
further length increments. In general, the original 
decrease is due to reduction of form drag and the 

‘‘ A streamlined body is one so shaped that the transformation 
of velocity head into pressure is so gradual that separation 
does not occur at all or only on a very small region at the 
extreme end.®^ 


subsequent increase is due to increase in skin friction 
drag resulting from the larger wetted surface. The 
length of a cylinder with blunt ends that will give 
minimum drag is approximately three times the di- 
ameter but this ratio does not remain true with other 
shape changes. Other considerations besides the drag 
alone are involved in proportioning a desired volume, 
such as manufacturing simplicity, handling, and re- 
lease or launching limits on dimensions and similar 
matters. Among low-drag projectiles the United 
States Shoe Machinery Hydrobomb, Design No. 8, 
has a length-to-diameter ratio of 4.65 ; the Westing- 
house Hydrobomb, 7.15; the Mark 13 torpedo, 7.18; 
the Mark 14-1 torpedo, 11.7; and the Mark 15 tor- 
pedo, 13.7. (See Chapter 13.) When a slenderness 
ratio of length divided by diameter is being chosen, 
it is sometimes convenient to express the drag co- 
efficient as a function of volume V, rather than of 
cross-sectional area. In this case 

Cdv (12) 

-v^V^ 

Comparison of this coefficient for different body 
shapes will provide an indication of the optimum 
proportion for a body of a given volume. The ordi- 
nary expression will not reveal this. 

It is possible to have a nose with a higher drag than 
that of a flat plate. A hollow hemisphere with the 
hollow side upstream has a drag about 19 per cent 
higher.®^ 

Seemingly small roundings of sharp edges meeting 
the flow head-on result in material drag reductions. 
If rounding is carried to the extent of putting a hemi- 
sphere on the upstream end of a cylinder 3 diameters 
long, the drag coefficient will be reduced to approxi- 
mately 0.25 at R about 3X10®, with similar reduc- 
tion for longer cylinders.®^ Still greater refinements of 
nose shapes are, of course, possible. Many so-called 
families, such as the spherogives, have been investi- 
gated and numerous noses based on special formulas 
have been designed and tested. The effect of some 
representative noses on the drag coefficient of a 
specific projectile will be described below in connec- 
tion with other components. 

Reduction in drag, as must be apparent, is ob- 
tained by reducing the violence of flow changes. Bet- 
ter noses lessen this violence at the forward end of the 
projectile and better afterbodies will improve condi- 
tions at the rear. Nose improvements, however, are 
relatively much more important than rear-end 




DRAG 


189 


changes when both conditions are bad, but this state- 
ment is not necessarily true under other conditions. 
Thus, as mentioned above, the addition of a hemi- 
spherical nose to a 3-caliber cylinder gave a Cd of 
0.25; the addition of a tapered afterbody while the 
nose remained “square,” gave 0.70. The combination 
of a hemispherical nose and hemispherical afterbody 
reduced the drag coefficient to 0.135.^^ This indicates, 
again, the importance of the type of flow around 
structural portions behind the nose in the possibility 
of percentage improvement. It is repeated that, un- 
less these parts are in high-velocity flow, changes mil 
have only a minor effect, if any. 

Interrelated Body, 

Afterbody, and Tail Influences 

Low-drag afterbodies are, compared to diameter, 
generally long and tapering^ since small changes in 
curvature are necessary so that the fluid may close 
smoothh" about the body. The taper ma}^ be a conical 
surface or some curved surface such as an ogive. 
When it is conical, there is customarily a transition 
curve connecting it to the cylindrical body portion. 
There is also, generally, a truncated end of relatively 
small diameter. Some afterbodies have booms, that 
is, small diameter cylindrical extensions, for the usual 
purpose of getting the tail surfaces into a more ad- 
vantageous position. The Mousetrap projectiles have 
rather long booms; the Squid, a shorter one. 

As mentioned in Chapter 9, tails may consi st of vanes 
alone, vanes with rudders, vanes with shroud rings, 
vanes with rudders and shroud rings, and other de- 
signs such as box tails. Some rockets have collapsible 
fins while, of course, spin-stabilized rockets have no 
tails at all in the sense the word is here used. Tail di- 
ameters are usually the same as the body but there 
are numerous exceptions, particularly some rockets 
which have very large diameter vanes. The primary 
purpose of the tail is to give stability and control. It 
is obvious that the tail should be no larger or more 
complicated than necessary to function adequately 
as anything additional will be only a disadvantage. 
The large wetted area (some 37 per cent in the case of 
the Squid) of the tail surfaces contributes materially 
to the skin friction drag, while the numerous sharp 
edges in the flow produce a form drag which may also 
be a considerable part of the total for the projectile. 


^ For a sphere at > 3 X 10% Cd has been given by Rouse 
35 0.20 and for a l-to-3 ellipsoid at /^ > 2 X 10% Cd = 0.06. 


Merely rounding all leading edges in the tail of one 
Squid model reduced the total drag by 20 per cent. 
Shroud rings will add unnecessarily to the drag unless 
they are constructed with the optimum angle to the 
flow at their location. This angle is not yet calculable 
from formulas and has generally been determined by 
polarized light flume observations checked, subse- 
quently, by water-tunnel performance tests. (See 
Chapter 3.) 

High-velocity flow must pass over or along all tail 
surfaces for these surfaces to have maximum effec- 
tiveness. This means that the afterbody design must 
be such as to direct it there and that the opening be- 
tween any shroud ring and the afterbody be large 
enough to permit its free flow through the tail. 

The “body” is generally a cylindrical portion be- 
tween the planes where the nose curvature becomes 
zero and where afterbody curvature begins. These 
sections may be short or long. Increased length of 
body section, other things being equal, increases the 
total drag mainly by the additional skin friction. In 
rare cases there have been projectiles with abrupt 
changes of diameter in the body section (unrelated to 
the nose or afterbody). Such changes will, of course, 
have an effect on the drag. 

As an example of the interrelation and effect of 
various components on the drag coefficient, we may 
consider some investigations of the British Squid 
(depth bomb). 

Figure 3 shows an outline drawing of the proto- 
type, of another model with a special nose, new cone 
afterbody and new tail, and of an earlier type nose 
referred to as the No. 45 nose. There were, actually, 
two new tails; they were alike except that one had a 
0-degree shroud ring (a true cylinder) while the other 
had a conical ring with a 2-degree cone angle. All 
parts were interchangeable except that the new 
tails could be used only with the new afterbody 
and the prototype tail only with the prototype 
afterbody. 

The upper graph of Figure 4 shows the influence of 
nose shape on the drag coefficient with variation of 
Reynolds number for the 0-degree tail models. Meas- 
urements extended to = 4X10® and the lines were 
extrapolated therefrom to full-scale values. The top- 
most three lines are, from the top, for progressively 
better noses all with the new afterbody and new 0- 
degree tail. They show progressively lower drags, 
particularly at full-scale R. The lowest curve of this 
group was obtained by the simple substitution of the 
special nose on the original model and gave the best 




190 


EFFECTS OF PROJECTILE COMPONENTS 




Figure 3. Outline drawing of British Squid and major modifications. 


results of any combination tried. This nose profile is 
based on the formula 



The lower graph is, similarly, for the same three 
noses and the new afterbody with 2-degree tail. A 
similar reduction in drag was also obtained. It may be 
noted that the 2-degree tail gave, with each nose, a 
lower drag than the 0-degree tail, the afterbodies be- 
ing the same. 

The cone afterbody with 0-degree tail was inferior 
to and, with the 2-degree tail, no better than the 
original afterbody and tail when all were used with 
the prototype nose. It is believed this is due to in- 
sufficient clearance between the shroud ring and new 
afterbody but it has not yet been checked experi- 
mentally. 

It should not be deduced from these curves that an 
improvement in nose shape will always result in pro- 
portionally less drag as R is increased. The opposite 
effect seemed to hold in a similar series of nose tests 


for the Mark 13-1 torpedo. Of course, an improve- 
ment with nose refinement occurred at any R in both 
cases. The difference in the two cases is that the per- 




CYLINDRICAL 

TAILS 

(ob 





PROlilTYPE 

uzo 

oaG 






_PR01 

ro Nosi 

1 1 

r 

20h 

lEp 

^B 

/wtTr 

NUM 

MOLU 

BER 

5 

'0 

QI5 

OK) 

■ — --- 




^^^PHERe 
SPFr.iAi ^ 

NO! 


CONE 4 

B 





Spec 


tes 


P«oro7^ 

^ Lj 

cont 

A8 







cone' TAILsI (2* 

) 













PRO- 















fiiset 



NOS 










SPE^ 

nose 

tip 

— _ 










QD III I 1 LJ L_ 

10* 2 3 4 6 8 K) 15 20 25 


REYNOLDS NUMBER 
(AB » AFTERBODY) 

Figure 4. Influence of nose shape on Cd with varia- 
tions of Reynolds number for British Squid and modi- 
fications. Top: Cylindrical tails (0 degree); bottom: 
Cone tails (2 degrees). 


INFLUENCE OF YAW 


191 



Figure 5. Effect of yaw on Cd and Cc for British Squid and modifications. 


^ (J)Nf’TDt:NTrAL ) 


192 


EFFECT OF PROJECTILE COMPONENTS 


centage improvement increased with R for the Squid 
and decreased for the Mark 13-1. The explanation is 
believed to be as follows. Granted a perfect afterbody 
and tail structure, the form drag coefficient for those 
parts would have an absolute minimum value. Form 
drag improvement, therefore, would be confined to, 
and dependent upon, the nose shape. A blunt nose will 
have a relatively high form drag and, hence, there 
will be a greater opportunity for its reduction at 
higher Reynolds numbers. Finer noses, producing 
less turbulence, have less opportunity to improve at 
higher velocities. The Mark 13-1 afterbody has a low 
form drag compared to that of the Squid afterbody, 
hence, the effects are akin to those produced by the 
perfect afterbody and tail. When a fine nose is used 
with the Squid afterbody and tail, the nose form drag 
is decreased but there is also more turbulence near 
the tail which will be reduced by the more advanta- 
geous flow conditions produced there at high Rey- 
nolds numbers. 

A discussion of drag under conditions of cavitation 
appears in the chapter on cavitation. 

6 INFLUENCE OF YAW OR PITCH 

ON DRAG AND CROSS FORCE OR LIFT 

Previous discussion has dealt with drag when the 
projectile had a zero pitch and yaw angle. Under 
these conditions, both the cross force and lift force 
will be zero for symmetrical projectiles. However, 
some degree of asymmetry will exist in individual 
projectiles, designed to be symmetrical, because of 
manufacturing tolerances, deformations from han- 
dling, and similar causes. If it be anticipated that such 
unintentional asymmetries will have a materially ad- 
verse effect upon projectile performance, they may be 
avoided by setting the tail vanes at a slight angle, as 
in the case of the British Squid, which produces a 
slow rotation of the projectile, thereby averaging out 
the effects. Rudders may be considered as devices 
intended to produce asymmetry for purposes of 
course control of the projectile and will, by their 
action, also overcome the effect of other unintended 
asymmetry. 


When the projectile yaws or pitches, a different 
aspect of the shape is presented to the flow, almost 
always one which will have a greater resistance. The 
effect of positive yaw angle to 10 degrees on the drag- 
coefficient is shown in the lower graph of Figure 5 
and on the cross force coefficient in the upper graph. 
All curves shown are for the Squid. Since the design 
of this projectile is symmetrical, the lift-coefficient 
curves plotted against pitch angle would be the same 
as those for the cross force coefficient. 

Values for negative yaw and pitch angles generally 
are the same as for positive angles except that the 
cross force coefficient will be negative. 

In general, a model with a lower drag at 0-degree 
yaw will also have a lower drag at greater positive or 
negative angles, although this is not invariably the 
case as may be seen even in the illustrative group. 
These drag-coefficient vs yaw-angle curves are, 
essentially, parabolas. 

10.7 effect of PROJECTILE COM- 
PONENTS ON CROSS FORCE AND LIFT 

Serious study of the effect of projectile components 
on the cross force and lift has been limited mainly to 
a consideration of the effect of horizontal and vertical 
rudder action and of fins and shroud ring at the tail. 
Numerous specific illustrations of their effect are 
given in this volume, particularly in Chapters 8 and 
9. In general, the most important requirements are 
that the fin and rudder surfaces be sufficiently large 
and arranged in the most effective locations and pro- 
portions to achieve necessary stability and control 
without introducing unnecessary drag. The latter 
can be further avoided by rounding all edges, as 
previously mentioned. Properly designed shroud 
rings are often, but not invariably, a material aid in 
course control. These matters are intimately con- 
nected with the moment coefficient about the center 
of gravity and are discussed further under that sub- 
ject. 

A comprehensive study of the effects of all the 
various components on cross force and lift is now 
being made but the results are not ready for report. 


Chapter 11 

EFFECT OF PROJECTILE COMPONENTS ON DAMPING AND 

DYNAMIC STABILITY 


111 INTRODUCTION 

T he behavior of a free-flying, nonspinning pro- 
jectile without rudder controls depends entirely 
on its dynamic stability and on the motion of the 
fluid through which it is traveling. The behavior of a 
controlled projectile also depends on these factors 
and, in addition, on the characteristics of its controls. 
To evaluate the dynamic stability of a tail-stabilized 
projectile it is necessary first to determine at least 
four of its hydrodynamic coefficients; namely, the 
coefficients of lift, moment, damping force, and damp- 
ing moment. It can be shown theoretically that, for 
normal projectile shapes, these four coefficients are 
intimately related, and that the damping coefficients 
may be determined without direct measurement if 
the lift and moment coefficients are known. Also, the 
dynamic stability is a simple function of the lift 
and moment coefficients. It is obvious that these re- 
lationships, if substantiated by experiment, would 
materially reduce the volume of preliminary tests 
and investigations required in order to design a pro- 
jectile shape to meet given performance specifica- 
tions. 

It is the purpose of this chapter to indicate the 
relationships among the various hydrodynamic co- 
efficients and their relationship to the dynamic 
stability of tail-stabilized projectiles; also, to show 
which of the various components of the projectile 
shape are the main factors in determining the hydro- 
dynamic characteristics of the projectile. 

DAMPING FORCE AND DAMPING 
MOMENT 

Definition 

When a projectile is traveling rectilinearly under 
steady-state conditions, the forces acting on it are 
functions of the velocity and angle of attack alone. 
However, when the projectile is oscillating or turning 
about a transverse axis, the forces acting on it are no 
longer determined by the velocity and instantaneous 
angle of attack alone, but are modified by reactions 
whose magnitudes depend on the instantaneous value 


of the angular velocity. For convenience in dealing 
with this latter case, the forces are resolved into two 
terms, one of which is equal to the force that would 
act if the projectile were traveling on a straight line 
with the same angle of attack at the center of gravity, 
and one which depends on the angular velocity. The 
sense of the second term, called the damping term, is 
always such as to oppose the angular velocity, thus 
changing the force system from a conservative system 
to one having energy dissipation through a “hysteresis 
loop.” 

1.2.2 Mechanics of Damping 

When the projectile deviates from rectilinear mo- 
tion, the angle of attack is no longer constant but 
varies from point to point along the axis. The flow 
about the body is then different from that of straight 
motion and, consequently, the forces are different. 
The method used in estimating the damping forces is 
based on the knowledge that, although the angular 
velocity modifies the force distribution about the en- 
tire body, the only changes which affect the resultant 
force occur at the tail. 

Figure 1, taken from reference 7b, shows the theo- 
retical force distribution about the bare hull of an 
airship in curved flight through a frictionless fluid, 
resolved into three terms. Part A shows the attitude 
of the ship in relation to its path, with bow turned 
inward and stern outward, and with yaw angle \l/ at 
center of hull. The first term of the force distribution, 
shown at B, is the same as in straight flight with 
angle of attack This gives rise to a destabilizing 
moment (tending to increase the yaw angle) but has 
no resultant force. The second term C, sometimes 
called the “negative centrifugal force,” is due to the 
fact that the ship, traveling with its bow turned into 
the curve, displaces air in an outward direction and is 
subject to a reaction directed inward. This is most 
pronounced at the middle of the hull. The third term 
D, represents forces concentrated near the ends, and 
their sum in magnitude and direction is equal to the 
lateral component of the centrifugal force of the dis- 
placed air. These forces are due to the fact that the 
angle of attack at the bow is smaller than x}/, while at 


193 


194 


EFFECT OF PROJECTILES ON DAMPING, DYNAMIC STABILITY 


the stern it is larger than \p. The sum of the second 
and third terms gives neither a resultant force nor a 
resultant moment. Thus, the resultant forces acting 
on the bare hull in curved flight in a frictionless fluid 
are the same as those in straight flight. 

The forces acting on a streamlined flnless body in 
rectilinear motion were analyzed in Chapter 8 of this 
volume. It was shown that in an ideal fluid such a 
body is subject to a destabilizing moment but de- 
velops no hft, and that in a real fluid the flnless body 
does develop some lift and that the destabilizing mo- 
ment is smaller than in an ideal fluid. It was also 
shown that the lift developed in a real fluid is due to 
vortices forming near the tail and, therefore, the lift 



attack at the tail. For the motion shown in Figure 
lA, the angle of attack at the tail is larger than that 
at the center. The lift, therefore, would be larger than 
for rectilinear motion with the same angle of attack 
at the center. This increase in the lift is, by definition, 
the damping force, and the moment of the damping 
force about the center of the hull is the damping 
moment. 

“ ^ * Estimate of Damping Coefficients 
from Steady -State Data 

The projectile in Figure 2 is shown moving in the 
direction of its axis with velocity v and, in addition, is 
turning about a transverse axis through the center of 
gravity with a small angular velocity co. The center 
of pressure of the tail force CPt then has a small 
downward velocity coX, and the angle of attack at the 
tail is tan“^ oik/v, where X= the distance from CG 



F 


X 







Figure 2 

to CPt. For small disturbances from the mean path, 
the angle of attack may be taken as coX/z; radians, and 
the force due to that may be taken as proportional to 
the angle of attack. The damping force then is 


Figure 1 . Airship in curved flight and forces developed. 

of the flnless body should be considered as acting at 
the tail. When fins or other tail surfaces are added, 
the additional lift developed by them also acts at the 
tail. It may be said, therefore, that for a streamlined 
body with tail surfaces the total lift acts at the tail 
and is determined by the effective angle of attack at 
the tail. 

In the preceding analysis of the curved motion of a 
flnless hull in a frictionless fluid it was shown that the 
body is subject to a destabilizing moment equal to 
that of rectilinear motion with the same angle of 
attack at the center of the body. The problem of deal- 
ing with the curved motion of a streamlined hull with 
fins in a real fluid may be greatly simplified by re- 
solving the forces into two terms: the theoretical 
moment of the hull, which is a function of the angle 
of attack at the center of the hull; and a lift force 
acting at the tail, which is a function of the angle of 


F = 


-C^A, 

V 2 


(1) 


where Ci = (d/ da) C l, or the slope, in units per radi- 
an, of the curve representing the coefficient of lift, as 
measured in the water tunnel or wind tunnel, plotted 
against the angle of attack a. The moment of this 
force about CG is the damping moment, which may 
be written 

K = F\ = —C,-^A\. (2) 

V 2 


If we define a damping force coefficient Cf, and a 
damping moment coefficient Cr as 


Cf = 
Ck = 


F 

^pvcoAl 

K 

^pvojAP 


(3) 

(4) 


where p is the density of the fluid, A the maximum 


DYNAMIC STABILITY OF PROJECTILES 


195 


cross-sectional area of the projectile, and I its overall 
length, then we get 


Cf = Czy — CieT, 

(5) 

Ck = Clifff = 

(6) 


where er is the eccentricity of the tail force. 

To determine the damping coefficients it is neces- 
sary, therefore, to know the slope of the lift curve and 
the eccentricity of the tail force. The latter may be 
evaluated when both the lift and moment coefficients 
are known, as outlined in Chapter 8 of this volume. 

The oscillating projectile in Figure 2 is shown at 
the instant when the angle of attack at CG is zero. 
When the angle of attack at CC is not zero, there are 
the normal cross force and normal moment due to the 
angle of attack at CG and, in addition, the damping 
force and damping moment due to the fact that the 
angle of attack at the tail is different from that at CG 
by + 03\/v. For computations involving oscillations 
about zero yaw, the damping coefficients are de- 
termined from the slope of the cross force coefficient 
curve and the eccentricity of this force at zero yaw. 
For oscillations about a definite angle of attack, such 
as when a torpedo is traveling with dynamic lift or 
when circling, the slope and eccentricity should be 
taken at the mean value of the angle of attack. 

In the preceding analysis, the contribution of the 
drag force to the moment was neglected. For low- 
drag projectiles and for small angles of attack, the 
error introduced by this omission is very small. Actu- 
ally the normal component of the hydrodynamic 
forces is (L cos a D sin a), where L is the cross 
force, D is the drag, and a is the angle of attack. For 
small values of a this may be taken as (L + Da) = 
}/ 2 PV^A(Cl + Cooi). In equations (1), (2), (5), and 
(6), Cl then becomes 

Cl = ^Cl + Cd. 

da 

DYNAMIC STABILITY 
OF PROJECTILES 

Any object in motion is said to be stable if it tends 
to continue in its present mode of motion. In ballistics 
we are usually interested in directional stability, i.e., 
whether a projectile, fired or launched in a given di- 
rection, continues to travel close to the original line 
of motion. When any projectile is disturbed from its 
line of motion it does not actually return to the origi- 


nal line, but the motion may be considered stable if 
the deviation is small. With respect to stability re- 
quirements projectiles may be divided into three 
groups: (1) spin-stabilized; (2) tail-stabilized without 
rudder control; (3) tail-stabilized with rudder con- 
trol. The stability of spinning projectiles is treated in 
Chapter 15 of this volume. In the following para- 
graphs we will discuss the stability of tail-stabilized 
projectiles such as bombs, rockets, and torpedoes. 

Although the stability requirements of rudder-con- 
trolled projectiles usually differ from those of rudder- 
less projectiles, the degree of dynamic stability in 
either case is determined without reference to rudder 
action. That is, the dynamic stability of a rudder- 
controlled projectile is determined by its hydrody- 
namic properties with rudders fixed in neutral 
position. 

Definition 

A projectile is said to be dynamically stable if, 
when disturbed from its linear motion, it will return 
to motion on a straight line without benefit of rudder 
action. The new line of motion is not an extension of 
the original line, but makes some angle with it. The 
magnitude of this change in direction depends on the 
degree of dynamic stability, the greater the stability 
the smaller the course deviation. 

A projectile that is dynamically unstable, when 
disturbed from linear motion, does not (in the ab- 
sence of rudder control) return to motion on a 
straight line. Instead, it travels on a gradually 
tightening spiral and eventually settles down to cir- 
cular motion. The diameter of the circle depends on 
the degree of dynamic instability, the greater the 
instability the smaller the diameter of the circle. 

As a corollary of the above definition it may be 
said that a dynamically stable projectile without 
rudder control cannot run on a circle. With rudder 
control a dynamically stable projectile can be made 
to circle, but can be brought back to linear motion 
merely by returning the rudder to neutral position, 
i.e., without applying opposite rudder. To bring a 
dynamically unstable projectile out of circular mo- 
tion, it is necessary to apply opposite rudder. Return- 
ing the rudder to neutral position would merely in- 
crease the diameter of the circular path. 

11.3.2 Criteria for Dynamic Stability 

A criterion for the dynamic stability of a projectile 




196 


EFFECT OF PROJECTILES ON DAMPING, DYNAMIC STABILITY 


may be derived very simply from a consideration of 
the conditions required for equilibrium on a circular 
path. This is based on the principle that any devia- 
tion from a straight path may be regarded as a 
tendency to swing into a circular path.^“ If the pro- 
jectile (with rudders, where present, locked in neu- 
tral position) can attain equilibrium on a circular 
path, then it is dynamically unstable. If it cannot 
attain equilibrium on a circular path, it will return to 
linear motion and, therefore, is dynamically stable. 

In Figure 3 is shown a projectile, with rudders 
locked in neutral position, traveling on a circular 
path of radius R, with velocity v and with angle of 
attack a (exaggerated in the figure) at CG. The forces 
are resolved into the theoretical moment of the bare 
hull H and a lift force acting at the tail. This tail 



force includes the normal lift L and the damping 
force F. In addition there is the centrifugal force 
Miv^lR acting at CG. Mi stands for the mass of the 
projectile M plus the apparent mass for longitudinal 
motion kipV, where V is the volume of the pro- 
jectile, and A:i the coefficient of apparent mass for 
longitudinal motion. The correct value of the ap- 
parent mass in this case is (A:i cos^ oi-\-k 2 sin^ a) pV,^^ 
but for small angles of attack kipV may be used. 

For equilibrium on the circular path, we have 

L + F - = 0, (7) 

H — \{L -|- F) cos Q! = 0. (8) 

For small values of a, 

L = Cl^A = Cia^A, 

H = Ch~AI = Chcc^AI. 

From equations (3) and (5) 

F = Cf^coAI = Cier^VoiAl. 


We define a mass coefficient mi such that 

Ml = 

Substituting in equation (7) and dividing by pv^A /2, 
we get 

Cia + CiCt-I — ~ “k (Cier — = 0 

V IX Jx 

I 

{mi — CieT)-p 

a = — (9) 

Substituting in equation (8) and dividing hypv^Al/2, 
we get 


Chct — CrCia 


\6t~Ci — 0 
V 


R 


erCi 


“ Ck- erC,' 

Equating (9) and (10) and solving for CiCt, we have 
miCh 


CiSt = 


-f- Cu 


( 11 ) 


It is seen that for equilibrium on a circular path, 
CiBt [ — Cf, from equation (5)] must have a definite 
value. If this requirement is fulfilled, the projectile 
will be indifferent to angle of attack and to circling 
radius as long as the angle of attack is within the 
limits wherein the forces are proportional to it. That 

is, the projectile may travel with zero angle of attack 
in which case R would be infinite, or it may assume 
some small angle of attack and circle on a radius corre- 
sponding to that angle of attack. If CiCt has a value 
greater than that indicated in equation (11), that is, 
if the moment of the tail force is larger than required 
to balance the hull moment, then the path of the pro- 
jectile will straighten out. If Cier is smaller, the 
angle of attack will continue to increase until it ex- 
ceeds the value wherein the forces are proportional to 

it. Since for large angles of attack Ci increases faster 
than linearly, equilibrium will be established eventu- 
ally and the projectile will continue to circle. 

It is apparent, therefore, that the condition repre- 
sented by equation (11) marks the borderline be- 
tween dynamic stability and instability, and may be 
used as a criterion. That is, for dynamic stability 


Cier — 


miCh 
+ Ch 


> 0 . 


( 12 ) 


Taking the ratio of the two sides of equation (11) we 
get another criterion which is somewhat quantitative 
in that it shows the ratio of the actual tail moment 


DYNAMIC STABILITY OF PROJECTILES 


197 


{CiCt) to that required to just barely attain dynamic 
stability, i.e., for dynamic stability 
eteT{mr+ C,) 

miCh ^ 

The value of these criteria lies in the fact that it is 
not necessary to measure the damping force and 
damping moment, but only the so-called static lift 
and moment. Also, the quantity on the right side of 
equation (11) may be evaluated as soon as the shape of 
the projectile body and its overall weight are selected, 
and before any tests are made. This tells us how large 
the quantity CiCt = Cf must be in order to attain 
the desired degree of dynamic stability. Since data 
are available on the moment and lift coefficients of a 
large number of projectile shapes with various tail 
structures, it should be possible to select a tail 
structure which, when mounted on the given pro- 
jectile, will produce very nearly the desired degree of 
dynamic stability. 

Another criterion for dynamic stability of ships 
and projectiles, developed by a different method from 
the one used above, has the form^^ 

CiCk - rnCm > 0 (14) 

where Ci, Cm, and Ck are as defined in this chapter, 
and m = mi — Cf. By substituting for Cm, Cf, and 
Ck their equivalents as indicated in this chapter, i.e.. 
Cm = Ch — Cier, Cf = Cier, and Ck = CiBt^, this 
expression may be reduced to equation (12). 

It should be noted that the dynamic stability of a 
projectile depends not only on the overall shape of 
the projectile, but also on its mass and on the density 
of the medium through which it travels. The stability 
criteria of equations (13) and (14) contain hydrody- 
namic coefficients Ci, Cm, Cf, Ck, and bt, and a mass 
coefficient Wi. For projectiles operating at high Reyn- 
olds numbers, the hydrodynamic coefficients are 
functions of the body shape alone. The mass coeffi- 
cient, however, depends on the mass and shape of the 
projectile and also on the density of the surrounding 
fluid, since 

M -f kipV 
- h.pAl 

where M = mass of projectile, ki = coefficient of 
apparent mass for longitudinal motion, p = density 
of fluid, A = maximum cross section, I = overall 
length and V = volume of projectile. For elongated 
projectiles ki is small (0.01 to 0.05). The value of mi, 
therefore, is nearly proportional to M, and inversely 
proportional to the density of the surrounding fluid, 


p. Examination of equation (14) shows that the dy- 
namic stability decreases with increasing mass of 
projectile, and increases with increasing density of 
the fluid. Thus, for instance, an aircraft torpedo 
which may be dynamically stable during its under- 
water run may not possess sufficient stability for its 
air flight. This is usually overcome by adding larger 
tail surfaces (air stabilizer) which are stripped off the 
torpedo on water impact. 

11.3.3 Relation between Static 

and Dynamic Stability 

The static stability of a projectile is determined by 
its shape alone, i.e., it is independent of the mass of 
the projectile or the nature of the fluid through 
which it is traveling. A projectile is said to be 
statically stable if, when restrained from moving 
laterally and given an initial yaw angle, the pro- 
jectile tends to return to zero yaw. The projectile 
is said to be statically unstable if the moment 
resulting from the initial yaw angle is such as to 
tend to increase the yaw. (In accordance with the 
sign convention used in this volume, a projectile is 
statically stable if Cm, the derivative of the moment 
coefficient, is negative, and it is statically unstable if 
Cm is positive.) The static stability in itself, there- 
fore, merely describes the behavior of a projectile if 
it were used as a weathercock but it does not describe 
its behavior in free flight, while the dynamic stability 
does indicate in a general way the behavior of the 
projectile in free flight. Nevertheless, for a projectile 
of given shape and weight traveling through a given 
fluid, the dynamic stability and static stability are 
directly related. 

The relation between the static and dynamic sta- 
bilities of a projectile will be illustrated by using, as 
an example, the Mark 14-1 torpedo without pro- 
pellers. The test data used herein are shown in Figure 
4, and are taken from water tunnel tests made on a 
propellerless model of the Mark 14-1 torpedo.^^ Only 
one of these curves, the one showing the moment co- 
efficient of the Unless body in an ideal fluid, was cal- 
culated. All others are test results. Taking the slopes 
of these curves for small pitch angles (±1°), we get 
the values of (7^ for the finless hull in an ideal fluid, 
and of Cl and Cm for the finless hull, hull with fins, 
and hull with fins and ring tail, in a real fluid. 

With Ch, Cm, and C i known, the eccentricity of the 
tail force, er, may be evaluated for each case. With 
bt known, the damping coefficients Cf and Ck may 




198 


EFFECT OF PROJECTILES ON DAMPING, DYNAMIC STABILITY 



be determined. Adding the value of the coefficient of 
mass my (for this torpedo in salt water mi =2.04), 
we can evaluate the criteria of dynamic stability of 
equations (13) and (14). Table 1 shows all these 
values, as well as C t, the derivative with respect to 
pitch angle of the coefficient of moment about CG due 
to the tail force (Ce = Ch — Cm),forthe finless body, 
body with fins, and body with fins and ring tail. It is 
seen that for these three conditions, respectively, the 
tail force acts at points 48, 50, and 51 per cent of the 
overall length aft of CG. If we take an average value 


Table 1. Hydrodynamic properties of Mark 14-1 torpedo 
without propellers. 


Coefficient 

Hull alone 

Hull with fins 

Hull with 6ns 
and ring 

Ck 

1.50 

1.50 

1.50 

Cm 

1.26 

0.78 

0.43 

Ct 

0.24 

0.72 

1.07 

Cl 

0.50 

1.43 

2.09 

er 

0.48 

0.50 

0.51 

Cf 

0.24 

0.72 

1.07 

Ck 

Cierinii -|- Ch) 

0.12 

0.36 

0.54 

m\Ch 

0.24 

0.83 

1.24 

CiCk - MCm 

-2.21 

-0.51 

+0.71 



for ct, in this case 0.50, then all the hydrodynamic 
properties of the projectile listed in Table 1 become 
linear functions of the lift coefficient derivative Ci. 

Figure 5 shows the variation of the different hydro- 
dynamic coefficients of the Mk 14-1 torpedo as 
functions of C i. The condition Ci = 0 is equivalent to 
the Unless hull in a frictionless fluid, which is subject 
to a pure moment Ch. As Ci grows, the stabilizing 
moment due to it grows and the resultant moment. 
Cm = Ch — CiCt, diminishes. Cf, Ck, and the dy- 
namic stability criteria of equations (13) and (14) 
increase linearly with Ci. It is seen that dynamic 
stability in water is reached when Cz = 1.77 [CiCk — 
mCm = 0 or Cier (my -}- Ch) ImyCh = 1], and static 
stability is attained when Ci = 3.0 {Cm = 0). To 
attain dynamic stability in air this torpedo would 
require a Cz of 3. Coincidentally, in this case, the 
same value of Ci gives both static stability and dy- 
namic stability in air. In general, the value of Ci 
required for dynamic stability in air does not differ 
much, for most projectiles, from that required for 
static stability. This forms the basis for the arbitrary 
rule that aircraft bombs and rockets must be 
statically stable. 

:nti 


EFFECT OF VARIOUS COMPONENTS 


199 


The values of Ci actually measured in the water 
tunnel for this torpedo are indicated in Figure 5. It 
is seen that neither the hull alone nor the hull with 
fins are dynamically stable in water. It is believed 
that, with propeller drive, this torpedo when 
equipped with fins is dynamically stable in water. 
The hull with fins and ring would be dynamicall}^ 
stable even without propeller drive. 



a 

7 

6 

S 

4 

3 

2 

I 


1 

2 
3 


5 

6 

7 

8 


Figure 5. Hydrodynamic properties as functions of 
lift coefficient derivative. Mk 14-1 torpedo without pro- 
pellers. 


EFFECT OF VARIOUS COMPONENTS 

From the preceding analysis it is clear that the 
damping and dynamic stability of normal, tail-stabi- 
lized projectiles are directly related to the static 
stability. By normal 'projectiles is meant relatively 
clean bodies of revolution, with fairly streamlined 
nose shapes (hemisphere or finer), with lift-producing 
appendages at the tail only, i.e., without fins, spoilers, 
Kopf rings, or any other prominent appendages 
ahead of the tail. For these projectiles it may be said 
that any modification of the body shape which in- 
creases the lift force, or shifts the point of application 
of the lift force aft along the body, also increases the 
damping coefficients and the dynamic stability. The 
effect of such modifications on the damping and dy- 


namic stability may, therefore, be inferred from their 
effect on the steady-state forces measured in the 
water tunnel or wind tunnel. 

^ ^ Nose Shape 

Measurements made in the water tunnel on a tor- 
pedo model with several different nose shapes rang- 
ing from a hemisphere to a 23 ^-to-I ellipsoid, and in- 
cluding the standard noses of the Mark 13 and Mark 
14 torpedoes, showed that the lift and moment co- 
efficients were practically unaffected by the nose 
shape.^^ Similar tests with other projectiles gave the 
same results. It may be concluded, therefore, that the 
damping and the dynamic stability of a projectile 
will vary but little with changes in nose shape, as 
long as the nose is a fairly streamlined body of 
revolution. 


Afterbody 

The afterbody shape has a pronounced effect on 
the hydrodynamic properties of the projectile. In 
Chapter 8 of this volume it was shown that the lift 
of a finless body is due to separation and vortex for- 
mation near the tail. It is evident, therefore, that any 
modification of the afterbody which increases the 
vortex formation will also increase the lift of the fin- 
less hull. It is known that abruptly tapering or trun- 
cated afterbodies produce higher lift than finely 
tapered shapes. When fins are added, the effect of the 
afterbody shape on the total lift depends on the loca- 
tion of the fins with respect to the zone of flow separa- 
tion. If the fins are within that zone, the flow velocity 
over the fins will be low and, consequently, the lift 
developed by them will be low, and this may more 
than offset the increase in the lift of the bare hull. 
This usually occurs on a torpedo with a rapidly taper- 
ing afterbody, since the fins are located aft of the 
zone where separation on the afterbody begins. On 
the other hand, with a rocket, where the fins are 
usually attached to the cylindrical portion of the 
body and the tapering or abrupt termination of the 
afterbody occurs abaft the fins, the fin lift is not re- 
duced by the separation while the body lift is 
increased thereby. 

^4 4 3 Tail Structure 

The use of stabilizing surfaces on nonrotating pro- 
jectiles was treated in Chapter 9 of this volume, 


^ niMlDENTIAT^ 



200 


EFFECT OF PROJECTILES ON DAMPING, DYNAMIC STABILITY 


where the effect of the various design factors on the 
lift and moment coefficients was shown. Again, any 
modification of the tail structure which increases the 
lift or the static stability of the projectile also in- 
creases the d3mamic stability. 

Propellers 

On propeller-driven projectiles, the propellers have 
a pronounced effect on the lift and moment acting on 


the projectile. This is partly due to the fact that the 
flow velocity over the tail structure is increased, but 
mainly because the propeller itself produces a trans- 
verse force or lift when yawed in the stream.^® Tests 
made on such projectiles without running propellers 
do provide valuable information for their design. 
However, any measurements made to determine ac- 
curately the hydrodynamic properties of the com- 
plete projectile should be made ^\^th power-driven 
propellers. 


Chapter 12 

EFFECT OF EXPERIMENTAL VARIABLES ON AN AIR-LAUNCHED 

PROJECTILE TRAJECTORY 


D uring the development of the plans for 
initiating launching studies for the purpose of 
investigating the water entry of projectiles, con- 
siderable thought had been given to the technique 
required for making laboratory studies in order that 
the results would be applicable to field conditions. 
The following section is devoted to the discussion of 
some of the conclusions that have resulted from 
these considerations. Two different points of view 
present themselves in the consideration of such a 
laboratory study: (1) that the study should be 
organized as a “model study” of specific projectile 
shapes and characteristics; (2) that the study should 
be an investigation and a clarification of the physical 
phenomena involved. At first glance it would appear 
that these two viewpoints would be quite widely 
separated. However, further consideration shows 
that, in general, satisfactory model experiments are 
possible only in case the experimenter has a good 
qualitative or semiquantitative understanding of the 
physical phenomena. The philosophy back of the 
ideal model experiment is that experiments shall be 
carried out under conditions that are similar in all 
respects to those existing in the prototype. This is 
strictly possible only in very rare cases, usually those 
in which only one simple physical process takes place. 
For the average case, however, the study involves the 
simultaneous action of several different physical pro- 
cesses, and analysis generally shows that the condi- 
tions for similarity of the model and the prototype 
are different for the different phenomena involved. 
The result is that practically all model studies have 
to be carried out under conditions in which the simi- 
larity laws and certain of the existing phenomena are 
disregarded completely. Under such conditions suc- 
cessful results can be obtained only if the experi- 
menter is in a position to evaluate the relative 
importance of each phenomenon involved. He must 
also be enabled on this basis to devise an experiment 
in which similarity is obtained for all of the major 
phenomena and is violated only for minor phe- 
nomena. 

In many cases the experimenter is not in this ad- 
vantageous position. He is then forced, if he is to 
carry on a sound program, to carry on his experi- 


ments with both objectives in mind, that is, to study 
the problem so as to delineate and evaluate the phe- 
nomena involved and as this knowledge becomes 
available, to proceed as rapidly as possible to the 
determination of the various specific results desired 
for the given prototype condition. A consideration of 
the knowledge available concerning some laboratory 
and field studies of the water entry of air-launched 
projectiles indicates that it is in this latter condition 
that there is not enough information available con- 
cerning the relative magnitude of the various factors 
which affect water entry to make it possible to plan a 
laboratory model study with assurance that the re- 
sults will be applicable to prototype conditions. 
Therefore, it seems inevitable that the work must be 
carried on step by step, gaining knowledge as rapidly 
as possible concerning the physical processes involved 
and applying it to the study of known projectiles as 
fast as the knowledge becomes available. 

Certain conditions can be established in the be- 
ginning. The study is basically a dynamic one, i.e., 
the study of the motion of a free body under the ac- 
tion of a system of forces. From this fact it follows 
that as the dynamic characteristics of the body must 
be carefully controlled, i.e., the specific gravity, the 
center of gravity, and the moments of inertia about 
the three axes, these are the properties of the 
body that determine its reaction to the force sj^stem. 
The greatest lack of knowledge apparently comes in 
the delineation and evaluation of the different forces 
that operate during entry. Cavitation studies in the 
water tunnel have much in common with the studies 
of the projectile behavior in entrance bubbles. Cav- 
itation studies have shown very clearly the extreme 
importance of precise geometric similarity of the 
body shape. It has been found that small deviations 
from true contours can, under certain conditions, 
have very significant effects on the magnitude and 
direction of the forces acting on the body. This means 
that a very precise workmanship is required for the 
construction of the bodies to be tested in the labora- 
tory, accompanied by precise measurements of the 
completed bodies. Tunnel tests have also shown that 
bubble shapes may be affected by small surface 
irregularities or changes in texture. All of the force 


201 


202 


EFFECT OF EXPERIMENTAL VARIABLES 


measurements in the water tunnel have demonstrated 
that the force system on such bodies is very sensitive 
to axial asymmetries or misalignments, i.e., to nose 
or tail structures that are out of line with the main 
body axis. An analysis of experimental data from 
various sources representing both laboratory and 
field investigations shows that the behavior of a body 
at water entry is greatly affected, both by the angle 
of a trajectory with respect to the water surface and 
by the pitch or yaw of the projectile with respect to 
its trajectory. This means that a laboratory study to 
investigate satisfactorily the entry problem must be 
in position to control accurately these variables and 
to obtain any desired combination of them at will. 
Some of the problems of a laboratory model study at 


water entry were pointed out in Chapter 2 in con- 
junction with the description of the controlled-at- 
mosphere launching tank. The most serious difficulties 
arise from the fact that water entry is a two-phase 
problem, i.e., it concerns both a gas and a liquid. 
This means that it is extremely difficult to set up ex- 
perimental conditions which will not be affected by 
the size or scale of the experiment. It is clear that the 
gas density, gas pressure, liquid viscosity, and surface 
tension are all factors that can affect the force system 
acting on the entering body. It is felt that the possi- 
bility of successful model studies depends, to a large 
degree, upon the experimenter’s ability to secure 
sufficient knowledge concerning these factors to 
enable him to evaluate their relative importance. 


Chapter 13 

TORPEDOES 


151 INTRODUCTION 

U NDER THE TERM “torpedoes’’ are included all 
those underwater projectiles which, throughout 
their underwater run, travel under their own power 
and are continuously guided by devices which main- 
tain or regulate their course and depth. Investiga- 
tions in this laboratory are confined almost exclu- 
sively to the exterior ballistics, which are not affected 
by the interior construction of the torpedo, the type 
of power plant (turbine, reciprocating engine, electric 
motor, or jet propulsion), or the type of steering 
mechanism control. For these investigations the most 
convenient classification is by method of launching 
into two groups: aircraft torpedoes and totally 
water-borne torpedoes. 

Aircraft Torpedoes 

Aircraft torpedoes are launched from aircraft 
traveling at high speed and relatively high altitudes, 
and as a result, they have a long air trajectory and 
hit the water at a high velocity. The impact opens 
up a cavity in the water which fills with air forming 
an elongated bubble which travels with the torpedo 
to a considerable depth, eventually separating and 
rising to the surface in a series of smaller bubbles. Upon 
emerging from the entry-bubble cavity, the torpedo 
rudders and propellers become effective, causing the 
torpedo to recover from the dive and finally to level 
off to its normal steady run. 


Totally Water-Borne Torpedoes 

Totally water-borne torpedoes are launched from 
submerged tubes or from the decks of surface vessels. 
In the latter case the air trajectory is relatively 
short, the impact velocity low, and the dive shallow. 
Hydrodynamic investigation of these torpedoes is 
limited to those characteristics affecting the under- 
water run only. 

Figure 1 shows, to the same scale, outline drawings 
of all of the torpedoes investigated. Table 1 shows 
weights and principal dimensions. The various tor- 
pedoes are briefly described in the following para- 
graphs. For fuller description, detail dimensions, and 
discussion of the test results, reference is made to 
specific reports covering each torpedo. 


^ ^ Aircraft Torpedoes 

Mark 13 Series 

All the torpedoes of the Mark 13 series have identi- 
cal body shapes and dimensions. The various modifi- 
cations differ from each other in the weight of the 
explosive charge, the running speed, and in the tail 
structure. The original Mark 13 torpedo had its rud- 
ders mounted aft of the propellers, supported by 
struts extending from the outer edges of the fins 
which were forward of the propellers. This arrange- 
ment was abandoned because of the inherent struc- 


Table 1. Dimensions and weights of various torpedoes. 


Overall Maximum Maximum 

length diameter weight Displacement Speed 

in inches in inches in pounds in pounds in knots 


Aircraft torpedoes 


Mark 13 series 

161 

Mark 25 series 

161 

Hydrobomb; Westinghouse design 

160.125 

Hydrobomb; USMC Design No. 30 

119.37 

Hydrobomb; USMC Design No. 8 

130 

Water-borne torpedoes 


Mark 14 series 

246 

Mark 15 series 

288 

Mark 26 series 

245.88 


22.42 

2127 

1703 

33.5-40.5 

22.42 



40.5 

22.42 

2360 

1770 

40 

28 



61 

28 

3500 

2052 

61 

21 

3185 

2516 

30.5-47.5 

21 

3847 

3045 

27.4-46 

21 

3350 

2630 

39-45 



203 


204 


TORPEDOES 








MK 14-1 TORPEDO 





MK 26 TORPEDO 


40 

SCALE, INCHES 


Figure 1, Outline dimensions of torpedoes. 



tural weakness and the added drag. It was super- 
seded by the Mark 13-1 in which the rudders are 
forward of the propellers, and immediately aft of the 
fins. Later modifications increased the speed and 
weight of explosive and strengthened the afterbody, 


without, however, changing the external dimen- 
sions. In other modifications, shroud-ring tails were 
added to improve the stability and behavior in water 
entry. Figure 2 shows the principal dimensions and 
Figure 3 is a photograph of the 2-in. diameter model. 





INTRODUCTION 


205 


Mark 25 Torpedo 

This torpedo has the same overall dimensions and 
body shape as the Mark 13. It was designed struc- 
turally to withstand drops from aircraft at higher 
speeds and altitudes than were possible with the 


ings, both with and withopt shroud rings, to deter- 
mine the arrangement which would cause least inter- 
ference with rudder and propeller action. Figure 4 
shows the model with the exhaust opening in one of 
the fins and Figure 5 shows the tail structure with 
one of the subsequent modifications in which the 



HORIZONTAL RUDDER 




Mark 13-1. It is equipped with a later design of 
power plant in which the exhaust gases, instead of 
discharging through a hollow propeller shaft, are dis- 
charged through two passages in the fins. In addition 
to the usual hydrodynamic tests, the investigation 
covered various arrangements of the exhaust open- 



Figure 4. Mark 25 torpedo model with exhaust open- 
ing in top of fin. 


gases are discharged through a stack attached to the 
shroud ring. 

Hydrobomb— Westinghouse Design 

This is a jet-propelled torpedo having the same 
overall length and diameter as the Mark 13 and the 
Mark 25. The nose is somewhat sharper and the 
afterbody has a more abrupt taper than the Mark 13. 
The fins and rudders for both course and depth con- 
trol aie considerably larger than on the Mark 13 or 


206 


TORPEDOES 


Mark 25. The depth control fins are symmetrical and 
have a total span 2 in. greater than the maximum 
body diameter. The course control fins are unsym- 
metrical, the lower fin projecting 1 in. beyond the 
maximum body radius and 1 in. more than the upper 





Figure 5. Mark 25 torpedo with ring tail and single 
exhaust pipe. 


fin. The fins are of appreciable thickness (2 in. maxi- 
mum) and both fins and rudders have rounded edges 
and are well streamlined. No modifications of this 
shape were tested. Figure 6 shows the outline dimen- 
sions, and Figure 7, a photograph of the model. 


Hydrobomb— United Shoe Machinery Corpora- 
tion Design No. 30 

This hydrobomb is jet propelled and intended to 
travel at an underwater speed of 60 knots. It is 119 
in. long and 28 in. in maximum diameter; shorter and 
of greater diameter than the Westinghouse design. 
The fins are relatively thick (2)^ in. maximum) and 
are larger compared to the body size than on the 
Westinghouse design. The maximum thickness of the 
fins is at about 80 per cent of their length from the 
leading edge. The rudders are relatively smaller than 
on the Westinghouse design, particularly the vertical 
or course rudders. The nose is a long (3.43 to 1) 
ellipsoid and the afterbody tapers rather abruptly. 
Figure 8 shows the principal dimensions and Figure 9 
is a photograph of the model. 


Hydrobomb — United Shoe Machinery Corpora- 
tion Design No. 8 

This is also a jet-propelled hydrobomb, designed 
for an underwater speed of 60 knots. It is 130 in. 
long, 11 in. longer than the Design 30 and the after- 
body has a more gradual taper. The fins are some- 
what smaller relative to the body size than on the 





Figure 6. Outline dimensions, Westinghouse hydro- 
bomb. 



Figure 7. Two-in. diam. model of Westinghouse hy- 
drobomb. 

Design 30 and the rudders, both horizontal and 
vertical, relatively larger. Two fin arrangements 
were tested, differing in that the span of the hori- 
zontal or depth fins was 28 in. on one and 34 in. on 


COM IDFNTTAr 


INTRODUCTION 


207 





Figure 8. Outline dimensions, United Shoe Machinery Corporation hydrobomb, Design 30. 


the other; the vertical fin span was 28 in. on both. 
Both models were also tested with shroud rings 
added on the fins. Figure 10 shows the principal 
dimensions and Figure 11 is a photograph of the 
model with the 34-in. depth fin span and shroud ring. 

13.1.2 Water-Borne Torpedoes 

Mark 14 and Mark 15 Series 

The torpedoes of these two series are all 21 in. in 
diameter, made up with heads and afterbodies having 
the same external shape and dimension and are all 
equipped with identical fin and rudder assemblies. 
The only differences, externally, are in their overall 
length, due to the different lengths of their cylindrical 
midsections. Models of only one torpedo in each 
series, the Mark 14, Modification 1 and the Mark 15, 



Figure 9. Two-in. diam. model of United Shoe Machin- 
ery Corporation hydrobomb, Design 30. 


Modification 1, were investigated. Relative to the 
size of the body, the fin and rudder areas of these 
torpedoes are considerably smaller than on the air- 
craft torpedoes. Tests were also made on these models 
with shroud rings added to the fins. Figure 12 shows 
the outline dimensions of the two torpedoes and Fig- 
ure 13 is a photograph of the model of the Mark 14-1 
torpedo. 


:(>N I- ^ 


208 


TORPEDOES 




Figure 10. Outline dimensions, United Shoe Machin- 
ery Corporation hydrobomb, Design 8. 



Figure 11. Two-in. diam. model of United Shoe Ma- 
chinery Corporation hydrobomb. Design 8 with 34-in. 

depth fin span and shroud ring. 

Mark 26 Torpedo 

This torpedo is electrically driven, designed for 
speeds of 39 and 45 knots. In overall length and di- 
ameter it is the same as the Mark 14. It has a some- 
what blunter shape and the displacement is slightly 
greater than for the Mark 14. The original design as 
received in the laboratory showed an afterbody with 
eight fins and a shroud ring. The shroud ring had an 
overall diameter 2 in. less than the torpedo body di- 
ameter in order to clear the latching device in the 
launching tube. The fins were considerably longer 
than on the Mark 14 and 15 and the rudders were 
relatively larger than on the Mark 14 and 15. Three 
successive modifications of the fin structures were 
investigated by water tunnel tests. The original de- 
sign was designated by the laboratory as the Mark 
26-1. On the Mark 26-2, the shroud ring was 
omitted. On the Mark 26-3 the shroud ring and the 
four 45° fins were omitted. On the Mark 26-1, 26-2, 
and 26-3 the horizontal or depth fins are inclined to 
the longitudinal axis of the torpedo, the forward 
edges being raised so that the fins are at an angle of 
about 13^° to the torpedo axis, giving a slight down- 


rudder effect. On the Mark 26-4 the fins are all 
shorter than on the other three models and the depth 
fins are in the plane of the torpedo axis. The design 
was based on results of tests of other projectiles which 
indicated that the greater part of the stabilizing 
effect is obtained from the aft portion of the fins and 


C6 MK14-I MK 154 
WAR SHOT IOS.r I248L 

EX SHOT 107.5" 1 24.8- 



CENTER OF MK 14-1 I09.5l| VERTICAL FINS 6 

^BUOYANCY MK 15-1 130.2^ RUDDERS 

OVER-ALL LENGTH MK 14-1 246" , 

MK 15-1 288“ 



Figure 12. Principal dimensions of Mk 14-1 and 15-1 
torpedoes. 



Figure 13. Model of Mark 14-1 torpedo. 




4 110 . 875 :: p ' 

4 112.375" Pi 

4 245.875=^ > 


Figure 14. Outline dimensions of the Mk 26-2 tor- 
pedo. 

that the gain in stability by extending the fins for- 
ward is very slight. The fins on the Mark 26-4 are 
closely comparable to those of the Mark 14. The 
rudders on all four models are the same. Figure 14 
shows the outline dimensions of the Mark 26-2 tor- 
pedo. Figures 15 and 16 show the tail structures of 


TYPES OF TORPEDO STUDIES 


209 


the Mark 26-1 and Mark 26-4, respectively. Figure 
17 is a photograph of the model of the Mark 26-1 and 
Figures 18 to 21 -show photographs of models of the 
four different tail fin designs. 



SHROUD muQ 

Figure 15. Fins and rudders of the Mk 26-1 torpedo. 




Figure 16. Fins and rudders of the Mk 26-4 torpedo. 


13.2 types of torpedo studies 
' Water Entry 

The controlled-atmosphere launching tank^ was 
designed and built specifically for investigating the 
behavior of air-launched underwater projectiles dur- 
ing the water-entry phase. The methods used are 
described in Chapter 12 of this volume. Because of 
the similarity of the entrance bubble to the fully 
developed cavitation bubble (see Chapter 4), some 
knowledge of the behavior of the projectile in the 
entrance bubble may be inferred, at least qualita- 


tively, from observation of the cavitation character- 
istics of the projectile in the high-speed water tunnel. 
Pressure distribution measurements provide addi- 
tional information that is useful in understanding the 
behavior of the projectile during the entry phase. 

^ ^ Force Measurements 


The force studies made in the water tunnel on tor- 
pedo shapes include the measurement of drag, cross 



Figure 18. Model afterbody of Mark 26-1 torpedo. 




Figure 19. Model afterbody of Mark 26-2 torpedo. 

force, lift, and moment as functions of the pitch 
(angle of attack), yaw, and rudder angle. These tests 
are made under steady-state conditions and, there- 


Figure 17. Model of Mark 26-1 torpedo. 


210 


TORPEDOES 


fore, give directly only the steady-state hydrody- 
namic forces and moments, but not the damping 
forces and moments which arise when the projectile 
is rotating or oscillating about a transverse axis. The 
data thus obtained are sufficient for solving various 
problems not involving angular velocity, e.g., the 
power requirements, the degree of static stability, the 
ability of the torpedo to carry excess weight over 
buoyancy, and the pitch angle and rudder setting at 



Figure 20. Model afterbody .of Mark 26-3 torpedo. 

which the torpedo must travel in order to maintain a 
horizontal path under any given loading condition. 
The steady-state force and moment data form part 
of the information required in dealing with dynamic 


problems involving angular velocities. Reference is 
made to Chapter 11, in which the relationship be- 
tween the static and dynamic coefficients is discussed. 



Figure 21. Model afterbody of Mark 28-4 torpedo. 

For well-streamlined shapes, such as torpedoes, the 
cross force, lift, and moment coefficients are practi- 
cally independent of the Reynolds number. The drag 
coefficient, however, does vary materially with the 
scale of the tests and, therefore, the investigations 
usually include a study of the drag coefficient as a 
function of Reynolds number. 

The models for the force tests were complete in all 
details except for the omission of minor surface ir- 



RUDOERS NEUTRAL 


Figure 22. Comparison of lift coefficients, aircraft torpedoes. 


TYPES OF TORPEDO STUDIES 


211 


regularities and the omission of the propellers. The 
propellers were omitted because, unless driven at the 
proper speed, they would only obstruct and disturb 
the flow on the afterbody. The action of the propellers 
undoubtedly modifies to some extent the forces and 
moments acting on the torpedo. However, data 
taken on propellerless models are useful in studying 


torpedo behavior, in calculating certain equilibrium 
conditions, and in comparing the effect of modifica- 
tions in design. 

Lift, Cross Force, and Moment 
The lift, cross force, and moment characteristics as 



EFFECT OF 10* DOWN RUDDER ON 
PITCHING MOMENT 

Figure 23. Comparison of pitching moment characteristics, aircraft torpedoes. 



RUDDERS NEUTRAL 



COURSE RUDDERS 10* PORT EFFECT OF K)* PORT RUDDER ON 

CROSS FORCE 


Figure 24. Comparison of cross force coefficients, aircraft torpedoes. 





212 


TORPEDOES 



2 4 6 8 

YAW, DEGREES STARBOARD 

COURSE RUDDERS lO* PORT 


-ao2 


-QP4 


-ao6 


YAW. DEGREES STARBOARD 
2 4 6 8 

\t n &.' 30 ; 


^MK 13-1 




WEST HYtjRQi . 


^MK 25 


USMC NO. 8 


Figure 25. Comparison of yawing moment coefficients, aircraft torpedoes. 


10 


EFFECT OF 10* PORT RUDDER ON 
YAWING MOMENT 



08 


0.7 


06 


05 


04 


03 


02 


OI 


2 4 6 8 

PITCH ANGLE, UP, DEGREES 































L 









/ 

fj 









// 

/ 









y 


o 








/ 


z 

u 






// 




o 

li. 

ui 


M 

K 1! 

1-1^ 


tc 

^MK 26-4 

5 

o 

D 

^ 1 

(IK 26-2"-^ 

f/ 


'IldK 

14- 

-1 

LIFT 




£ 

( 









/y 















































020 


0.16 


012 


006 


0,04 






















z 




1 

MK 14-1 

1 ^ 




UJ 

o 




! 






5 







MK 

15-1 






MK 

26-4 











MK 2 

!6-2. 

V 
































2 4 6 8 

PITCH ANGLE, UP, DEGREES 


2 4 6 8 

PITCH ANGLE, UP, DEGREES 


RUDDERS NEUTRAL DEPTH CONTROL RUDDERS lO" DOWN 

Figure 26. Comparison of lift coefficients, water-borne torpedoes. 


EFFECT OF lO* DOWN RUDDER ON 
LIFT 


functions of positive pitch and yaw (upward pitch symbols used in these and succeeding figures are 
and starboard yaw), with rudders neutral and set at given in the Appendix, 

10 degrees down or port are plotted in Figures 22 to The differences in the force and moment character- 
25 for aircraft torpedoes, and Figures 26 to 29 for istics and rudder effect of the various torpedoes de- 
water-borne torpedoes. Definitions of the terms and pend not alone on the size of the fins and rudders, but 


TYPES OF TORPEDO STUDIES 


213 


also on the contour of the torpedo, the shape of the 
fins and rudders, and the interference effects be- 


tween the torpedo body and the fins and rudders, 
as well as the location of the center of gravity 



Figure 27. Comparison of pitching moment characteristics, water-borne torpedoes. 



RUDDERS NEUTRAL 


COURSE RUDDERS 10* PORT 


EFFECT OF 10* PORT RUDDER ON 
CROSS FORCE 


Figure 28. Comparison of cross force coefficients, water-borne torpedoes. 


4 




214 


TORPEDOES 



YAW, DEGREES STARBOARD 
RUDDERS NEUTRAL 



EFFECT OF K)* WRT RUDDER ON 
YAWING MOMENT 


Figure 29. Comparison of yawing characteristics, water-borne torpedoes. 



Figure 30. Relation between drag coefficient and Reynolds number, Mk 13-1 torpedo. 


of the torpedo. In comparisons of similar body 
shapes having stabilizing surfaces of considerably 
different areas, the larger surfaces produce more 
lift and a greater stabilizing moment. This is illus- 
trated by comparing the lift and pitching moment 
coefficient curves of the Mark 13-1 torpedo and the 
Westinghouse hydrobomb in Figures 22 and 23. The 
depth fins of the hydrobomb are much wider than on 
the Mark 13 torpedo and result in a greater increase 
of lift with pitch for the hydrobomb and a small de- 
stabilizing moment. In comparing the two United 


Shoe Machinery Corporation [USMC] designs of 
hydrobomb, the Design No. 8, with its larger fin area 
shows a similar difference in lift and moment. These 
comparisons, however, are not quantitative; that is, 
there is no direct relation between fin size and the lift 
or moment, even on very similar body shapes. The 
rudder effect is a function not only of the size of the 
rudders, but of their disposition relative to the fins 
and afterbody and of the shape of the rudders. One 
extreme example is the comparison of the effect of a 
10-degree port rudder on yawing moment between 


TYPES OF TORPEDO STUDIES 


215 


the USMC Design No. 30 and Design No. 8 hydro- 
bombs. On the Design No. 30, the course rudders are 
extreme!}" small* and located directly aft of rather 
thick fins, and show a very slight effect on the mo- 
ment at all yaw angles. In the Design No. 8, the fins 
are thinner and the rudders considerably larger, and 
the effect on the yawing moment is several times as 
great. 


Variation of Drag Coefficient with Reynolds 
Number 

Tests to determine the variation of the drag co- 
efficient as a function of Reynolds number were made 
on 13^-in. and 2-in. diameter models in the high- 
speed water tunnel at velocities between 10 and 70 
fps. Figures 30 to 33 show Cd as a function of R 



Figure 31. Relation between drag coefficient and Reynolds number, Westinghouse hydrobomb. 


tn in 



Figure 32. Relation between drag coefficient and Reynolds number, Mk 14-1 torpedo. 



Figure 33. Relation between drag coefficient and Reynolds number, Mk 15-1 torpedo. 

\:(>NF[ni:N'fTAT7^ 



216 


TORPEDOES 


plotted on logarithmic paper. It is evident that 
straight line extrapolation on these diagrams is all 
that is justified by the experimental data. As a com- 
parison, the von Karman curves for turbulent skin 
friction only, for flat plates of the same surface area 
and length as the torpedoes have been plotted in 
Figures 31, 32, and 33. If a power law is assumed for 
the variation of the drag coefficient with Reynolds 
number, it maj^ be expressed b}^ the equation: 

Cd = (1) 


If the coefficients inequation (1) are evaluated from 
the curves drawn on Figures 30 to 33, the resulting- 
equations are the following: 


Mark 14 torpedo 
Mark 15 torpedo 
Mark 26-1 torpedo 
Mark 26-4 torpedo 
Mark 13 torpedo 
Westinghouse hydrobomb 


Cz)=3.32/^-^'^ 
Cd = ZMR-^^^ 
Co=2.937^-®-'® 

Cz>=2.54/^-®20 
Cz> = 1 . 28 /?"^^^ 


The slope of the curves, indicated by the exponent 
of R, varies from about -Y? to - Vs, with most of the 
experimental data tending toward the negatively 
larger value, i.e., a steeper slope. The Reynolds 
number obtained at 60 to 70 fps with 2-in. diameter 
models is, for most torpedoes, between Ve and yi 2 of 
the Reynolds number corresponding to the prototype 
operating condition. The scatter of the test points 
is such that repeated experiments might easily justify 
a change in the slope exponents and, consequently, 
in the extrapolation to prototype conditions. 

The fineness ratio of a streamlined shape such as a 
torpedo is commonly expressed as the ratio of length 
to diameter, l/d. 

The drag coefficient Cd, usually calculated on the 
basis of the maximum transverse cross-sectional area, 
may also be calculated on the basis of volume V to the 
% power, resulting in the expression: 


CDy = 


D 




When calculated on this basis, the coefficient for a 
given Reynolds number shows less variation with the 
fineness ratio l/d. 

In Figure 34, the drag coefficients of most of the 
torpedoes investigated, calculated from the test re- 
sults on the basis of both area and volume, have been 
plotted as ordinates against values of l/d as abscissas, 


for a constant Reynolds number of 6X10®. It will be 
noted that the curve of Cdv vs l/d has a long flat 
minimum. This indicates that, for a given volume, a 
series of torpedoes could be designed, all having the 
same volume and requiring approximately the same 
horsepower to produce a given speed, but covering a 
wide range of length-to-diameter ratios. 

It must be remembered that these results are from 
a series of bodies all having good streamlining. Their 
resistance is largely due to skin friction, with a rela- 
tively small contribution of form drag. Changes in 
nose and afterbody profiles, and in the form of 
appendages such as tail structure, can affect appreci- 
ably the form drag and thus the overall resistance. 
Structural variations of this type account for the 
scatter of the points shown on Figure 34. 



Figure 34. Relation of drag coefficient to length/ 
diameter ratio for constant Reynolds number. 


Drag and Power Requirements 

The drag determined by model tests is useful in 
estimating the horsepower requirements of the full- 
size torpedo, even though extrapolation of the drag 
coefficient to prototype conditions may not be ver}- 


0:;u:^^^anKATl \i, 


TYPES OF TORPEDO STUDIES 


217 


exact. For propeller-driven torpedoes, if the propul- 
sion efficiency is known, it is possible to estimate the 
shaft horsepower required. Conversely, if the shaft 
horsepower of a given torpedo is known, the extra- 
polated drag coefficient curve makes it possible to 
estimate the propulsion efficiency. Thus in Figures 
30, 32, and 33 scales for propulsion efficiency are 
shown based on shaft horsepower measurements from 
dynamometer tank measurements. This calculation 
assumes that the drag force obtained by extrapolat- 
ing water tunnel measurements is a true indication of 
the propeller thrust required to drive the torpedo. 
This neglects the change in flow over the afterbody 
caused by the propeller. 

The following approximate expression may be used 
to estimate the shaft horsepower required by a well- 


tion to the ^4 to Vt power of the Reynolds number 
(see Figures 7 to 10). For simplicity, the Vs power 
was used, although Ve corresponds more nearly to 
most test results and would result in higher estimated 
power at high speeds. For a torpedo of a given size, 
therefore, if the drag coefficient varies as the —0.2 
power of the speed, the drag force is proportional to 
the 1.8 power of the speed and the horsepower to the 
2.8 power of the speed. Also, as shown by Figure 34, 
the drag coefficient, when computed on the basis of 
instead of cross-sectional area, is more nearly in- 
dependent of the shape and length-to-diameter ratio 
and is, therefore, assumed constant in the above for- 
mula. For convenience the displacement was used in- 
stead of the volume because data on torpedoes 
usually are given in terms of displacement (buoyancy) . 


Table 2. Calculated and observed horsepower of several torpedoes. 


Shaft horsepower 


Torpedo 

Displacement 
in lb 

Speed in 
knots 

Drag coefficient 
at rated speed 
from Figures 

30 to 33 

Calculated 

for 

65% prop, 
efficiency 

Calculated 

from 

equation (2) 

By test 
(average) 

Mark 14 

2430 

31.5 

0.107 

108 

105 

102 



46 

0.098 

309 

303 

325 

Mark 14-1 

2516 

31.5 

0.107 

108 

107 

102 



46 

0.098 

309 

310 

325 

Mark 15-1 

3045 

27.4 

0.122 

82 

82 

80 



34 

0.117 

149 

151 

142 



46 

0.110 

347 

352 

335 

Mark 26-1 

2630 

39 

0.110 

212 

200 




45 

0.106 

314 

300 


Mark 26-4 

2630 

39 

0.123 

237 

200 




45 

0.120 

355 

300 


Mark 13-1 

1765 

33.5 

0.071 

101 

100 

96 

Mark 13-2 

1765 

40 

0.068 

160 

165 

170 

Westinghouse hydrobomb 

1770 

40 

0.069 

163 

(jet propelled) 


streamlJhed, propeller-driven torpedo at speeds with- 
in present torpedo practice: 

hp = 0.369 X 10“^ (speed)^® (displacement)® (2) 

in which the speed is in knots and the displacement 
is in pounds. 

The constant 0.369 X 10“"^ of equation (2) was 
evaluated from data on the displacement, speed, and 
shaft horsepower from dynamometer tank tests of 
torpedoes of the Mark 13, Mark 14, and Mark 15 
series taken from U. S. Navy Ordnance pamphlets 
629A, 635, and 642, respectively. 

The form of the above equation was chosen be- 
cause drag tests show that the drag coefficient is not 
constant but varies approximately in inverse propor- 


Table 2 shows the comparison for several torpedoes 
of the shaft horsepower (1) computed directly from 
the extrapolated drag coefficient assuming a propul- 
sion efficiency of 65 per cent, (2) calculated from 
equation (2), and (3) as determined by dynamometer 
tank tests. 

Equilibrium Running Conditions 

The weight of a torpedo is normally greater than 
its buoyancy, and the center of gravity CG is usually 
ahead of the center of buoyancy CB and slightly be- 
low the axis of symmetry. Therefore, in order to 
travel on a horizontal path, the torpedo must assume 
a pitch angle and a rudder setting such that the lift 




218 


TORPEDOES 


will balance the excess weight over buoyancy and the 
hydrodynamic moment will balance the static mo- 
ment due to the displacement of CG from CB. For 
any given conditions of speed, weight, and CG loca- 
tion, there is only one pitch angle and one rudder 
setting which will satisfy these conditions. The fol- 
lowing paragraphs present one of several methods 
for determining the pitch and rudder angles required 
for equilibrium. 



Figure 35. Forces acting on torpedo in straight run. 


Figure 35 shows the forces acting on a torpedo 
when running on a straight horizontal path with a 
pitch angle a. The hydrodynamic forces are resolved 
into a lift L acting at right angles to the path, a drag 
D acting parallel to the path, and a moment M. The 
lift and drag are taken as acting at the point 0, on the 
torpedo axis and above the center of gravity. In 
addition, there is the propeller thrust T assumed to 
be acting along the axis, the weight W acting verti- 
cally downward at the center of gravity, which is a 
distance y below the axis, and the buoyancy B acting 
vertically upward at the center of buoyancy, which 


is on the axis and a distance a aft of the center of 
gravitj^ The equilibrium equations may then be 
written : 


Vertical forces: L + B — IF + T sin a = 0. (3) 
Horizontal forces: D — T cos a = 0. (4) 

Moments about 0: M — Ba cos a —Wy sin 
a = 0. (5) 


From equation (4) 


T = 


D 

cos a 


Substituting for T in (3) and rearranging 
L + D tsin a = W - B. 


(6) 


Since both the distance y and the pitch angle a are 
small, equation (5) may be written 


M = Ba. 


(7) 


Dividing equation (6) hy}/if)V^A and (7) by }/ 2 P^^AI, 
we get 

^ ^ . IF-B 

Cl + Cd tan a = 


pv^ 


and 


Ba 


pv^ 


■Al 


Dividing (9) by (8), we have 
Cm 


Ba 


Cl Cd tan a (IF — B)l 


( 8 ) 


(9) 


( 10 ) 



Figure 36. Mk 15-1 torpedo. Pitch angle and rudder setting for equilibrium. 


TYPES OF TORPEDO STUDIES 


219 


To simplify the solution of the above equations, 
the water tunnel data is plotted in the form of Cm 
against the quantity {Cl + Cd tan a) as shown in 
Figure 36 and the constant pitch angle and constant 
rudder angle lines are drawn. Here Cm is the moment 
coefficient, Cl the lift coefficient, Cd the drag co- 
efficient, and Cd tan a represents the vertical com- 
ponent of the propeller thrust. The data shown in 
Figure 36 is for the Mark 15-1 torpedo and was 
taken from Figure 20 of the report on this torpedo^"* 
with the 1 -degree rudder setting intervals drawn in 
by interpolation. From equation (10) it can be seen 
that, for a given set of loading conditions, the locus of 
equilibrium points for all speeds on the diagram in 
Figure 36 is a straight line through the origin with a 
slope equal to 5a /(IF — B)L In order to determine 
equilibrium conditions for any speed it is necessary 
only to determine the quantity (Cl + Cd tan a) by 
means of equation (8) and to locate the correspond- 
ing point on the straight line locus of equilibrium 
conditions. The equilibrium values of pitch angle and 
rudder setting for the speed represented by the point 
so located can then be read directly from the pitch 
angle and rudder setting curves of the diagram. Fig- 
ure 36 shows the solutions for the Mark 15-1 at three 
different running speeds under conditions at the 
start of a run, i.e., fully loaded with fuel and ex- 
plosive. 

For a low-drag torpedo the term (Cd tan a) is 
small in comparison to Cl (about 5 per cent for the 
Mark 15) and, therefore, the solution for equilibrium 
conditions may be further simplified by neglecting 
the term and plotting Cm against C l instead of against 
(Cl “h Cd tan a). 

Table 3 shows the equilibrium pitch and rudder 
angles for several torpedoes calculated by the above 
method. 


Table 3. Equilibrium pitch angles and rudder settings 
for various torpedoes in straight horizontal run. 


Torpedo 

Speed Pitch angle, Rudder setting, 

in knots up, in degrees down, in degrees 

Mark 13-2 

40.5 

0.7 

1.1 

Mark 14-1 

45 

1.1 

3.1 


31 

2.2 

5.4 

Mark 15-1 

46 

1.2 

3.8 


34 

2.0 

5.6 


27.4 

2.9 

7.1 

Mark 26-2 

45 

0.8 

2.0 


39 

1.0 

3.3 

Mark 26-4 

45 

0.7 

3.2 


39 

1.0 

4.2 


^ ^ Pressure Distribution 

The forces acting on a projectile traveling through 
any fluid are due to the distributed fluid pressures 
acting normal to the surface, and to the shear stresses 
in the fluid adjacent to the surface (skin friction) 
acting tangentially. The tangential forces make up 
most of the drag, but the moment and cross force are 
practically unaffected by them. Therefore, with the 
pressure distribution about a projectile completely 
known, it is possible to calculate the resultant mo- 
ment, cross force, and lift, and also the contribution 
of the normal pressures to the drag (form drag). With 
most torpedoes, however, the pressures acting on the 
tail surfaces cannot be measured because of the thin- 
ness of these sections on the small models. Conse- 
quently, only the forces acting on the bare hull can 
be computed from the pressure distribution. 

Laboratory Procedure 

Two-inch diameter scale models were used for the 
pressure distribution measurements. Piezometer 
holes V 32 in. in diameter with the entrance edges 



Figure 37. Model of Mark 14-1 torpedo assembled on 
streamlined strut with base plate and tube manifold 
ready for installation in the water tunnel. 

rounded to 0.005-in. radius were drilled normal to the 
surface of the torpedo and each connected by a small 
rubber and nickel-silver tube to one side of a differ- 
ential pressure gauge. The other side of the gauge was 
connected to static pressure in the tunnel working 


220 


TORPEDOES 


section and the differential pressure read directly on 
a weighing beam-type balance reading to 0.01 psi. 
All piezometer openings were in a single plane through 
the longitudinal axis of the torpedo. The pressure 
distribution was explored by setting the plane of the 
piezometer openings at a given angle with the vertical 
and measuring the pressure at each tap for yaw angles 
of 0, ±3, and ±6 degrees. In most cases the angles of 
the plane of the taps were varied in 15-degree steps 
from 0 to 90 degrees from the vertical. Because of the 
symmetry of the torpedo, these measurements give 
the pressure distribution about the entire body. Most 
of the tests were made with a velocity of 40 fps and a 
static pressure of 10 psi. Tests at other velocities and 
pressures showed that within the range of the tests 
there was no measurable change in the relative pres- 
sure distribution. Figure 37 is a view of the Mark 
14-1 model mounted ready for test. 


Test Results 

The test results are presented in terms of 
where p — P — Po, 

p = normal pressure on the torpedo surface 
in pounds per square foot, 

Po = static pressure in undisturbed water at 
same level as torpedo centerline in 
pounds per square foot, 
q = pv'^/2 = dynamic pressure of water in 
pounds per square foot, 
p = mass density of water in slugs per cubic 
foot, 

V = mean relative water velocity in feet per 
second. 

Figures 38 and 39 show typical pressure distribu- 
tion and location of pressure taps for torpedo shapes 


CYLINDRICAL LENGTH 


'a 4 .'o 


OVER- ALL length MK 14-1 

246” 


^ MK 15-1 

288" 





Figure 38. Mk 14-1 and 15-1 torpedoes. Longitudinal pressure distribution on nose and afterbody at zero yaw. 




nnrxTTU. 


TYPES OF TORPEDO STUDIES 


221 



-r- 

10 


-r 

II 


1 I 1 1 T 

12 13 14 15 16 

LOCATION OF PRESSURE TAPS 




Figure 39. Mk 25 torpedo. Pressure distribution along longitudinal section at zero yaw. 


on a longitudinal section at zero yaw. Figure 40 
shows the effect of pitch or yaw on the pressure dis- 
tribution in a plane at right angles to the plane of 
pitch or yaw. Figures 41 and 42 show the effect of 
pitch or yaw on the pressure distribution in the pitch- 
ing or yawing plane, for the windward and lee sides 
of the Mark 14-1 torpedo. Figures 43 and 44 show 
the effect of pitch or yaw variation in pressure around 
the torpedo at points on the nose and afterbody. 

These measurements show two interesting common 
characteristics. First, the pressure on the body sur- 


face is higher than the static pressure in the undis- 
turbed fluid, Po, only over a small portion of the nose 
and a small portion of the afterbody and tail. Every- 
where else the pressure is less than Pq. Second, over 
the cylindrical body section the magnitude of the 
relative pressure, p/q, is seemingly unaffected by 
body length and is only slightly affected by the kind 
of nose and hence by pressures ahead of the midsec- 
tion. Figure 38 shows that with the same nose and 
afterbody shapes the pressure along the body cylinder 
of the Mark 14-1 and Mark 15-1 torpedoes is exactly 


222 


TORPEDOES 


the same. Comparison of Figures 38 and 40 show 
that despite the very much greater reduction in 
pressure on the spherical tip of the Mark 25 torpedo, 
ipjq along the cylinder is only —0.08 compared to 
—0.05 for the Mark 14-1. 

The minimum value of p / q obtained at the nose is 
a function of the nose profile and the consequent 
curvatures and accelerations of the flow around it. 
Note that if the torpedo operates under a combina- 
tion of velocity and submergence such that the mini- 
mum pressure P on the nose equals the vapor pres- 
sure Pv then 



where K is the cavitation parameter. Increasing 
numerical values indicate an increasing tendency for 
cavitation to occur early. 

In the examples shown p/g increases gradually 
along the afterbody section to slightly positive val- 
ues. The rate of increase and the final magnitude ob- 


tained depends upon the profile and the tendency, if 
any, for the flow to separate from the body surface. 
These measurements are all for well-streamlined 
afterbodies so that there is no discontinuity in the 
curves up to the point where the pressure is in- 
fluenced by the presence of the tail surfaces. Note the 
slight reduction in p/g, for all examples, caused by 
the sudden change in curvature at the transition from 
the cylindrical body to curved afterbody section. 

Pressure distribution data on torpedoes are use- 
ful mainly for determining the best location and 
arrangement for the pressure intake to the hydro- 
static diaphragm of the depth control mechanism. If 
this mechanism is to keep the torpedo at the set 
depth under all normal operating conditions, it is 
necessary that the pressure impressed upon the dia- 
phragm be at all times equal to the static pressure of 
the undisturbed water at the actual running depth of 
the torpedo. This is best accomplished by locating 
the pressure intake to the hydrostat at a point on the 
body where the pressure at the surface, under all 
conditions of speed, 3^aw, and pitch, is equal to the 




II 12 13 13 16 

LOCATION OF PRESSURE TAPS 




Figure 40. Mk 14-1 torpedo. Pressure distribution along longitudinal section at right angles to plane of yavv' or pitch. 


TYPES OF TORPEDO STUDIES 


223 



o 


II 12 13 15 16 

location Of PRESSURC TAPS 




Figure 41. Mk 14-1 torpedo. Pressure distribution along longitudinal section in plane of yaw or pitch. Windward side 
of body. 


static pressure of the water. Also, the intake opening 
should be flush with the surface, at right angles to it, 
and with smooth edges. Experience has indicated 
that piezometer openings with slightly • rounded 
edges (to a radius of about Ve the bore diameter) are 
more accurate and reliable than sharp-edged open- 
ings. 

With the pressure intake located where the pres- 
sure at the surface is not equal to the static pressure, 
the hydrostatic diaphragm would, for a given yaw or 
pitch angle, be actuated by a pressure which differs 
from true static by a fixed fraction of the velocity 
head. For a single-speed torpedo, the pressure im- 
pressed on the diaphragm would then differ from 
static pressure by a constant number of feet, and this 
can be taken into account in the calibration of the 
depth-setting mechanism. In a multispeed torpedo, 
this method of correction cannot be used since it 
would require a different calibration at each speed. 
Another method of correcting for mislocation of the 
pressure intake is to so design the intake that the 


pressure transmitted to the diaphragm differs from 
the normal pressure at the surface by the required 
fraction of the velocity head. This can be done by 
drilling the pressure taps at some angle other than 
normal to the surface or by using scoops or baffles. 
These methods, however, are likel}^ to be highly 
sensitive to changes in yaw or pitch. 

The requirements outlined above in connection with 
the location and design of the pressure intake for the 
depth control mechanism apply also to the pressure 
intake for the hydrostatic diaphragm of the depth and 
roll recorder [DRR], if the instrument is to record true 
running depth. 

Re-examination of the longitudinal pressure dis- 
tribution curves shows that the pressure at the sur- 
face equals the static pressure {p/q = 0) at two sta- 
tions on the bod}^, one on the head and one on the 
afterbody. The transverse pressure distribution curves 
show that on the afterbody, in the region near the 
station where p, q = 0 (e.g., stations 21 and 22, Fig- 
ure 44), the pressure is practically independent of 


\ coNr]\n:^T\ \i. ^ 


224 


TORPEDOES 


yaw or pitch. This position, therefore, meets the re- 
quirements for the location of the pressure intake for 
the depth control diaphragm. On the other hand, at 
the station on the forebody where p/? = 0, the pres- 
sure varies greatly with yaw or pitch (see stations 3 
and 4, Figure 43). Therefore, it is not advisable to 
locate the intake to the DRR diaphragm at that 
station. Remote connection of the DRR to the posi- 
tion on the afterbody where 'pjq = 0 will probably be 
ruled out because of the physical difficulties involved. 
It appears, therefore, that the best procedure re- 
mains to determine the error of the DRR, and to 
apply a correction to the depth record obtained with 
the instrument in its present location. 

It should be pointed out that unless the pressure 
intakes for both are located where the effect of pitch, 
yaw, and roll are negligible, the depth control mecha- 
nism and the depth and roll recorder should not be 
used as primary instruments to check each other, as 
in this case it is possible to have the torpedo run at 
some depth other than set depth and, at the same 
time, to obtain a depth record which indicates a run 


at or near set depth. As has already been mentioned, 
the pressure over most of the surface of the torpedo is 
lower than static pressure (see Figures 38 to 42). It is 
possible that the pressures impressed on both depth 
control and depth and roll recorder diaphragms are 
lower than static pressure. In this case, the torpedo 
would run below set depth but the DRR would indi- 
cate a depth shallower than the actual running depth; 
thus the error may not be detected. 

Cavitation 

The general phenomenon of cavitation on under- 
water projectiles, and the similarity between the fully 
developed cavitation bubble and the entrance cavity 
of air-launched projectiles, were discussed in Chapter 
4 of this volume. The effect of nose shape on the 
inception and development of cavitation is covered 
in Chapter 5. The effect of cavitation on the forces 
acting on the projectile is treated in Chapter 6, and 
Chapter 7 deals with the noise generated by cavita- 
tion on the underwater projectiles. For the purposes 


‘f 8 5 n ia is iT 

LOCATION OF PRESSURE 'PPS 




Figure 42. Mk 14-1 torpedo. Pressure distribution along longitudinal section in plane of yaw or pitch. Lee side of body. 


/ CO\i LOENTI AL 1 


TYPES OF TORPEDO STUDIES 


225 


Table 4. Cavitation parameter K for incipient cavitation on nose and tail structure, and speed in knots at 5-ft submer- 
gence above which further cavitation will develop. 


0 

Yaw angles in degrees 

3 

6 

Mark 13-1 torpedo 




Cavitation on nose 




A for inception 

0.73 

0.81 

0.89 

Speed in knots at 5 ft submergence 

34 

33 

31 

Cavitation on tail structure 




K for inception 

0.92 

1.46 

2.02 

Speed in knots at 5 ft submergence 

31 

24 

21 

Westinghouse hydrobomb 




Cavitation on nose 




K for inception 

0.31 

0.37 

0.41 

Speed in knots at 5 ft submergence 

52 

48 

46 

Cavitation on tail structure 




A for inception 

0.80 

0.86 

1.14 

Speed in knots at 5 ft submergence 

33 

32 

27 

Mark 14-1 torpedo 




Cavitation on nose 




A for inception 

0.34 

0.36 

0.38 

Speed in knots at 5 ft submergence 

50 

48.50 

47 

Cavitation on tail structure 




A for inception 

0.42 

0.74 

1.14 

Speed in knots at 5 ft submergence 

43 

33.50 

27 

Mark 26-4 torpedo 




Cavitation on nose 




A for inception 

0.38 

0.38 

0.44 

Speed in knots at 5 ft submergence 

49 

49 

46 

Cavitation on tail structure 




A for inception 

0.60 

1.00 

1.80 

Speed in knots at 5 ft submergence 

38 

29 

22 


of this chapter, it is sufficient, therefore, to indicate 
the specific reasons for studying the cavitation 
characteristics of torpedoes in particular. 

Cavitation on torpedoes during the normal part of 
the run is objectionable because of the sharp increase 
in drag with the development of cavitation, because 
of the detrimental effect on stability and control, and 
because of the noise generated by the formation and 
subsequent collapse of the cavitation bubbles. In 
addition, cavitation originating on the tail structure 
may spread to the propellers and interfere with their 
function. The various components of the torpedo 
should, therefore, be so designed that cavitation will 
not occur when operating under design speed and 
shallowest submergence normally used. This in- 
volves a study of the conditions leading to the in- 
ception of cavitation, which is normally carried out 
on each torpedo under investigation by this labora- 
tory. A study of the size and shape of the fully de- 
veloped cavitation bubble and its behavior when the 
projectile is yawed is also useful in understanding 
the behavior of aircraft torpedoes while in the en- 
trance bubble. 


The noses and forebodies of torpedoes running at 
underwater speeds up to 50 knots and even higher 
offer no difficult problems in design to avoid ob- 
jectionable cavitation. The tail structures, particu- 
larly the leading edges of the stabilizing fins and the 
attachments forming the supports for the rudder 
pivots, usually develop cavitation at lower speeds for 
a given submergence than the nose. At the higher 
speeds, unless set to run at considerable depth, the 
cavitation on parts of the tail structure may be suffi- 
cient to interfere seriously with the action of the 
rudders and propeller. Table 4 shows, for several of 
the torpedoes investigated, the speeds, at 5 ft sub- 
mergence, that are permissible to avoid nose or tail 
cavitation altogether. Considerably higher speeds, at 
the same submergence, are permissible before there is 
serious interference with steering or stability. This is 
illustrated by Figure 45 which shows, at 3° yaw, the 
visual appearance of cavitation on the Westinghouse 
hydrobomb at successively lower K values of 0.34, 
0.29, 0.25, and 0.18 corresponding respectively to 
speeds at 5-ft submergence of 50, 54.5, 58.5, and 69 
knots. At 50 knots, there would probably be a high 




226 


TORPEDOES 


level of cavitation noise, but no interference with 
rudder effect. At 54.5 knots the cavitation effects on 
the afterbody might affect the rudders and be suffi- 
cient on the forebody to increase the drag and affect 
the stability. The higher speeds, corresponding to the 
two lowest K values doubtless could not be obtained 
in underwater propulsion because of greatly increased 
drag and the entire change in hydrodynamic char- 
acteristics. 

^ Specific Modifications 

Several investigations were made to determine the 
effect on the hydrodynamics of certain torpedoes re- 
sulting from various modifications of their external 


shape. Some of these modifications were suggested by 
this laboratory or by others to overcome some unde- 
sirable characteristic such as high drag or insufficient 
stability, while other modifications were designed to 
meet some requirement apart from hydrodynamic 
considerations as, for example, suspension fittings 
designed to facilitate the installation of torpedoes in 
aircraft, or a modification of the exhaust gas dis- 
charge system. In these latter cases, the studies made 
in this laboratory were concerned with the possible 
effects of such modifications on the hydrodynamics of 
the torpedo. 

The most fruitful in this group of investigation was 
the one which led to the addition of the shroud ring 
to the tail structure of the Mark 13 series torpedoes. 


STATION 2 



160* 

140* 

120* 

100* 

8 

iO* 

60* 

40* 

20* C 

>* 

20* 

40* 

60* 

80* 

100* 

120* 

140* 

160* 

I8C 





























































n 








" 

- 51 ; 






















-4- 




















04 

















' 



























-X*- 

— 




























02 

04 



























































STATION 3 

























































Yi 

iW 

^NGl 





, 

N 










02 

























< 


























n 























0 ' 










































- 



















€r— 













-02 






"^1 



■—1 




r 

-X' 



























































-04 






































STATION 4 


2 

4 


-02 



-06 




Figure 43. Mk 14-1 torpedo. Pressure distribution about normal cross section. Stations on forward part of nose. 




TYPES OF TORPEDO STUDIES 


227 


STATION 6 

180* 160* 140* laO* 100* 80* 60* 40* 20* 0* 20* 40* 60* 80* 100* 120* 140* BO* 








L 




1 

I 


1 

1 






1 








































=i 






























— 









— 

















J_ 

























t=z-Sr=^t 




= tr 







^•=‘t 


0 




































1 














t= 
























; 

— Ct2 



















, 











— *1 




L. 










































I Y/|y ^ ^ 







Figure 44. Mk 14-1 torpedo. Pressure distribution about normal cross section. Stations on afterbody. 


Prior to this modification, these torpedoes ran some- 
what erratically, in that they often broached and 
hooked after entering the water, and had a periodic 
roll of considerable amplitude and a wavy depth line 
during the steady run. A preliminary study of the 
hydrodynamic characteristics of these torpedoes indi- 
cated that the broaching might be due to excessive 
instability with a consequent short turning radius 
and could be corrected by the addition of a shroud 


ring. This laboratory then investigated a systematic 
series of shroud rings for these torpedoes and recom- 
mended one of the designs tested. A model with this 
ring is shown in Figure 46. This ring was inst ailed on 
full-scale torpedoes which were fired at the Morris 
Dam Launching Range, and showed less tendency to 
broach and roll. Later test drops from aircraft at San 
Diego and at Newport confirmed these findings and 
the shroud-ring tail was finally adopted. 


228 


TORPEDOES 



Figure 45. Westinghoiise hydrobomb. Development 
of cavitation at 3 degrees yaw. (A) K =0.34, 50 knots at 
5 feet submergence. (B) K = 0.29, 54.5 knots at 5 feet sub- 
mergence. (C) K = 0.25, 58.5 knots at 5 feet submergence. 

(D) K = 0.18, 69 knots at 5 feet submergence. 

The addition of a shroud ring to the tail fins of a 
torpedo modifies the hydrodynamic characteristics of 
the torpedo in several ways. 

First, by increasing the tail surface area, the cross 
force at any angle of attack is increased. Since this 
increment of cross force is concentrated at the tail, it 
is evident that the resultant moment increment is a 
stabilizing one. Therefore, a torpedo with ring tail 
usually has less static instability than the same tor- 
pedo without ring. By the same reasoning, it may be 
concluded that the ring tail also increases the dynamic 
stability. 

Second, the ring usually decreases the roll ampli- 
tude and thereby reduces cross steering.^^ This is 
accomplished both by the increased resistance to roll 
due to the additional skin friction of the ring itself, 
but, mainly, by the increased effectiveness of the fins 
due to the prevention of circulation around their 
outer edges where they are covered by the ring. With 
reduced cross steering and increased stability, a 
smoother trajectory with respect to both course and 
depth line is obtained. 

Third, if the ring is so placed that it overlaps the 
rudders or comes very close to them, it may cause a 
change in the effectiveness of the rudders. This may, 
in some cases, be detrimental to control; in all cases 
this and the increased stability result in larger turn- 
ing radii. In the case of the Mark 13 series torpedoes. 


the shroud ring reduced the static instability to about 
one-half of its value without ring and the rudder 
effect to about 62 per cent of its former value.^^ 
This did cause an increase in turning radius^® but 
improved the overall performance on straight 
runs. 

Fourth, if the ring is so designed that it fits the 
flow lines about the afterbody of the torpedo, it 
should cause no appreciable increase in the drag. As a 
matter of fact, the ring may even reduce the drag 
somewhat by improving the flow around the after- 
body and by preventing separation. An improperly 
designed ring, however, may cause an appreciable 
increase in drag and a consequent reduction in speed. 

On the Mark 26 torpedo, several modifications of 
the tail structure, as suggested by this laboratory, 
were investigated by model tests (see Figures 18 to 
21). The original design embodied a shroud ring, but 
the limitation imposed, i.e., the reduced diameter, 
and the necessity of locating the ring forward of the 
rudder supports, were such as to place the ring too 
close to the afterbody and to cause it to interfere with 
the rudder effect. No beneficial action could be at- 
tributed to the ring, as was evidenced by the results 



Figure 46. Model of Mark 13-1 torpedo with shroud 
ring tail. 



Figure 47. Model of Mark 13-1 torpedo with 8 spades. 

of tests on the same model with the ring omitted. 
Also the original design had eight stabilizing fins, all 
considerably longer than on similar torpedoes which 



TYPES OF TORPEDO STUDIES 


229 


were known to operate successfully. Models with 
four of the eight fins removed, and one with the four 
remaining fins shortened were made and tested with 
the result that the last model, with the four shortened 



Figure 48. Model of Mark 13-1 torpedo with hem- 
ispherical nose and stabilizer ring. 


fins, showed hydrodynamic properties that indicate 
satisfactory running performance together with 
simpler fabrication in the prototype. 

Other specific modifications investigated were var- 
ious modifications of nose shapes on the Mark 13 
torpedo and attachments to the nose of various de- 
vices intended to improve the water-entry behavior. 



Figure 49. Model of Mark 13-2A torpedo with sus- 
pension band Mark 11. 

Two examples are shown in Figures 47 and 48. The 
effects of various suspension attachments to aid in 
aircraft launching were also investigated for the 
Mark 13. One version tested is shown in Figure 49. 

Numerous arrangements for discharging exhaust 
gases from the tail structure of the Mark 25 torpedo 
were studied, especially noting the cavitation per- 
formance and the combined effects of cavitation and 
gas exhaust on the action of the rudders and pro- 
peller. For the latter tests, a power model was tested 
in which the propeller was rotated at speeds corre- 
sponding to the propeller speed of a full-size torpedo. 


Chapter 14 

ROCKETS AND OTHER NONROTATING PROJECTILES WITH 
STABILIZING SURFACES 


GENERAL FEATURES 


14 2 7.2.INCH CHEMICAL ROCKET 


V ARIOUS FORMS of stabilizing surfaces applied to 
nonrotating projectiles were discussed in Chapter 
9. The general statements of principles therein pre- 
sented apply to stabilizing surfaces on rockets, al- 
though the selection of the particular form of these 
surfaces is subject to some necessary limitations and 
qualifications on account of the inherent properties 
of rocket projectiles. 

The shape of a fin-stabilized rocket and conse- 
quently its external ballistics vary according to the 
combination of the several components making up a 
rocket, namely, the explosive charge, the rocket 
motor, and the stabilizing device. The rocket motor 
shape depends on the size and type of the explosive 
charge and on the velocity required. The best form 
for the stabilizing device depends on the proportions 
of the charge and motor and the method of launching. 
For tube-launched projectiles the maximum dimen- 
sion of any component must be limited to the bore of 
the tube. One result of this is the folding-fin type of 
tail. For rack-launched units no such restrictions are 
necessary. If the combination of charge weight and 
range is such that a relatively small motor is neces- 
sary, it can be housed in a small diameter boom ex- 
tending aft from the main charge. Tail surfaces 
attached to such a boom were found in Chapter 9 to 
be very effective so that, in general, the maximum 
tail span or diameter can be held to a small dimen- 
sion. On the other hand, a projectile requiring a 
motor of the same diameter as the main charge intro- 
duces limitations in the stabilizing tail proportions. 
Interference from the body reduces the tail effective- 
ness so much that, in general, such units require tail 
spans exceeding the projectile diameter. 

The various fin-stabilized rockets tested in the 
laboratory were for a wide range of application and 
consequently included all types of shapes and ar- 
rangements of components. In the following sections 
will be reviewed briefly the various fin-stabilized 
rockets tested by this laboratory which are fairly 
representative of the varieties of rockets now in use. 
Profile diagrams of these rockets are shown in 
Figure 1. 


The following physical data apply to this pro- 
jectile: 


Body and ring tail diameter 
Ring tail length 
Overall length 
Weight without propellant 
Explosive charge 
Distance, nose to CG, the center 
of gravity (without propellant) 
Moment of inertia about CG 
Without propellant 
Radius of gyration 
Velocity 


7.2 

in. 

= 1 caliber 

4.0 

in. 

= 0.55 caliber 

45.25 

in. 

= 6.3 calibers 

47.9 

lb 


19.5 

lb 



0.391 X length 

65.7 lb-ft2 
1.167 ft 
680 fps 


This rocket is a good example of one having a ring 
tail no larger in diameter than the body of the pro- 
jectile. In effect the ring tail is mounted on a greatly 
extended boom. As discussed in Chapter 9, the 
mounting of the tail on a boom will increase effective- 
ness of the tail surfaces and, hence, the static stability. 

In Figure 1 is shown the outline of the original de- 
sign of this rocket Many tests were made to de- 
termine whether the addition of fins to the ring tail 
would increase stability. Three of the fin and ring 
tails, as well as the original design, are shown in the 
photographs in Figure 2. Figure 3 gives the cross 
force, drag, and moment coefficients for these four 
tail designs. 

From the curves it is seen that the addition of fins 
increases the stabilizing moment from 20 to 50 per 
cent. The great increase obtained with tail No. 67 is 
due to the additional length as well as to the fin sur- 
faces. It is interesting to note that tails No. 68 and 62 
have about the same stabilizing moment coefficient, 
showing that when fins are extended forward, the 
increase in moment is not at all proportional to the 
increase in fin surface. 


14 3 5-INCH HVAR ROCKET 


The following physical data apply to this pro- 
jectile: 


Overall length 
Maximum diameter 
Outside diameter of fins 
Length of fins 


68.60 in. = 13.64 calibers 
5.03 in. = 1 caliber 
15 in. = approx 3 calibers 
8 in. = approx 1.6 calibers 


230 




5-INCH HVAR ROCKET 


231 



60 MM MORTAR 



2.36 IN. ROCKET (BAZOOKA) 



0 


5 10 15 

SCALE. INCHES 


20 





Figure 1. Outline drawings of fin-stabilized rockets. 




232 


NONROTATING PROJECTILES WITH STABILIZING SURFACES 


Loaded weight 136.5 lb 

Weight without propellant 112.5 lb 
Radius of gyration 1.82 ft 

Velocity 1,375 fps 

Distance, nose to CG 0.467 X length 

As will be seen in the outline drawing, Figure 1, 
this rocket^^ is a bullet-shaped projectile with fins 
having a span greater than the body diameter. This 
is a most effective way to obtain a high stabilizing 
moment. The tests indicate that the moment in- 
creases much more rapidly with increasing span of 
the fins than with increasing fin length. This point is 
clearly illustrated in Figure 1 of Chapter 9 which 
shows the variation in moment coefficient with in- 



Figure 2. Ring and fin tails, 7.2-in. chemical rocket; 

reading down, tail 61, 62, 67, 68. 

creasing fin span and length. These curves indicate 
that practically no increase in stability is obtained by 
extending the fin length forward more than \]/2 
calibers. 

Eleven ring tails of widely differing proportions 
were tested in order to determine their performance 
compared to the fin tails. The ring type of tail has 
many advantages, especially from the standpoint of 
mechanical strength and smaller physical dimen- 
sions. In Figure 4 of Chapter 9 are given the moment 
coefficients for ring tails having diameters of 1.5, 2.0, 
and 2.5 calibers, and lengths up to 2.5 calibers. These 
curves show how rapidly the moment increases with 
increasing ring diameter and also that little increase 
in stability results from making the ring length more 
than one-half the ring diameter. 


In order to show more graphically the comparison 
of fin and ring tails. Figure 4 has been prepared. This 
gives the dimensions of fin and ring tails of different 
proportions, each of which produces the same mo- 
ment coefficient. Figure 5 is a photograph of a ring 
tail and a fin tail for the 5-in. HVAR rocket which 
produce the same moment coefficient. These draw- 



Figure 3. Force and moment coefficients; 7.2-in. 
chemical rocket. 

ings show very clearly that the ring-tail design is 
more compact. 

14 4 41^-inch rocket projectile 

The original design of this rocket^^’^® is shown in 
Figure 1 and in the photograph of Figure 6. The 
blunt afterbody was fitted with six collapsible fins 
which produced a fairly high stabilizing moment. As 


^< (>M'll)l \ I'l 


41^-INCH ROCKET PROJECTILE 


233 


this rocket was to be launched through a tube, the 
maximum fin span or ring diameter of the tail could 
not exceed the body diameter. For this reason collap- 
sible fins were used. An alternate collapsible-fin design 
is shown in Figure 7. 

It was felt that the reliability of the rocket could 
be increased if it could be stabilized by fixed surfaces 




ALL DIMENSIONS IN CALIBERS 
MOMENT COEFFICIENT FOR ALL TAILS =a225 
YAW ANGLE = 3* OVERALL LENGTH = I3J64 CALIBERS 

Figure 4. Fin and ring tails all having the same mo- 
ment coefficient. 

instead of the collapsible fins. As the ring type of tail 
seemed to offer the most possibilities, considering the 
limitations imposed by tube launchings, several of 
these designs were tested. Tail No. 24, shown in 
Figure 8, consisted of a 1.0-caliber diameter ring 0.89 
calibers long mounted on four vanes extending not 
far from the blunt afterbody. Tests indicated that the 
projectile was unstable with this tail due, no doubt, to 
the blunt afterbody preventing the diversion of much 
of the flow through the ring. 


In order to divert more of the flow through the 
ring, and thereby increase the stability, a ring tail 
1.0 caliber in diameter and 0.75 caliber long was 



Figure 5. Ring and fin tails for the 5-in. HVAR giv- 
ing equal moment coefficients. 



Figure 6. Four and one-half-inch rocket with No. 10 
collapsible fin tail. 



Figure 7. No. 25 collapsible fin tail for 4.5-in. rocket. 

mounted on booms of various lengths. Figure 9 shows 
this ring tail mounted on a boom 1.5 calibers in 
length. Many other combinations of ring, boom, and 


234 


NONROTATING PROJECTILES WITH STABILIZING SURFACES 


fins were tried, but the arrangement shown in Figure 
9 gave the greatest stability. 

In Figure 10 are shown the drag and moment co- 



Figure 8. Four and one-half-inch rocket with No. 24 
ring tail. 



Figure 9. Four and one-half-inch rocket with ring 
tail 0.75 caliber long on boom 1.5 calibers long. 















’"1 

FAIL 

NO. I( 

D 



















2 

5 








1 

1 











,30 


— 







— 

— - 


31 








24 
















boom (No. 30), and the same ring attached to a boom 
1.31 calibers in length (No. 31). These curves empha- 
size the fact that a ring tail of the same diameter as 
the projectile body, if mounted too close to the after- 
body, will produce little if any stabilizing moment. 



Figure 11 . Two and one-quarter-inch A A rocket. 

By mounting the ring on a boom, a good degree of 
stability can be obtained. It is seen from Figure 10 
that a ring 0.75 caliber long will produce practically 



Figure 12. Force and moment coefficients; 21^-in. 

AA rocket. 

the same stabilizing moment as the long-span collap- 
sible fins (Tail No. 10) if it is mounted on a boom a 
little over 1 caliber in length. 



Figure 13. Original design of 2.36-in. rocket. Conical 
nose and fixed fin tail. 


Figure 10. Drag and moment coefficients; 4.5-in. 
rocket with various tails. 

efficients for the projectile fitted with the original fin 
tail (No. 10), the fin tail attached by means of vanes 
(No. 25), the ring 0.89 caliber in length attached with 
fins (No. 24), the ring 0.75 caliber in length without a 


14 5 2K-INCH AA ROCKET 

The 234-in. AA rocket,^® shown in Figures 1 and 
11, is similar in design to the 5-in. HVAR rocket in 
that the fins are attached directly to the bullet- 
shaped body. The physical data of this rocket are as 
follows: 





2.36-INCH ROCKET (tHE BAZOOKa) 


235 


Overall length 
Fin span 
Fin length 
Velocity 


14.5 calibers 
2.8 calibers 
2,5 calibers 
680 fps 


The moment, drag, and cross force coefficients for 
this projectile are given in Figure 12. It is of interest 
to note that the curves in Figure 1 of Chapter 9, 
which show the moment coefficients for a family of 
fin tails for the 5-in. HVAR projectile, give practi- 
cally the identical value for the moment of a tail 
having the dimensions just noted above. 


6 2.36-INCH ROCKET (THE BAZOOKA) 

Many tests were made on models of this rocket, 
30,57-59 which is the well-known bazooka, in order to 
determine the effect on performance of various types 
of fin and ring tails as well as different nose shapes. 
In addition to the outline drawing in Figure 1 , photo- 
graphs of various modifications are shovm in Figures 
13, 14, and 16. This is a low- velocity, short-range 
rocket launched from a tube, and for these reasons 
the drag is relatively unimportant and tail design 
must be such that it will not exceed the body diam- 
eter. Figure 13 is a photograph of the original design 
of this rocket with conical nose and fixed-fin tail. 

Five designs of collapsible-fin tails, as shown in 
Figure 14, were tested. These were similar in that 
they consisted of six fins that could fold for passing 
through the launching tube and which opened in 
flight. These five tails had the following dimensions: 

Tail number Span of unfolded Vane angle back 
vanes in inches from radial 


1 


5° 

2 

7K 

5° 

3 

5^ 

40° 

4 

8 

40° 

5 

9.19 

28° 


Table 1 gives the data available on the force co- 
efficients for these collapsible-fin tails compared with 
the original fixed-fin tail. 


Table 1. Force and moment coefficients for 2.36-in. 
rocket with various fin tails. 



Drag 

Cross force 

Moment 


coefficient 

coefficient 

coefficient 

Tail 

Cd at 0° yaw 

Cc at 4° yaw 

Cm at 4° yaw 

No. 1 

0.52 

0.23 

-0.029 

No. 2 

0.95 


-0.022 

No. 3 

0.76 



No. 4 

0.77 



No. 5 

0.42 

0.37 

-0.092 

Original fixed fin 

0.30 

0.16 

-0.004 


The remarkable increase in the stabilizing moment 
obtained with the collapsible fins is in accord with the 
discussion in Chapter 9 where it was shown that the 
stability increases very rapidly with increase in fin 
span. As would be expected, the collapsible fins 
cause a great increase in drag, but this is of relatively 



Figure 14. Collapsible fin tails, 2.36-in. rocket. (A) 
Tail No. 1, (B) tail No. 2, (C) tail No. 3, (D) tail No. 4, 
(E) tail No. 5. 


rt jfTvni)i-vnt^ 


236 


NONROT ATIING PROJECTILES WITH STABILIZING SURFACES 


little importance because of the short range of the 
rocket. 

Partly on account of the high drag, but largely be- 
cause of the mechanical complication and fragility of 
the collapsible fins, an effort was made to design a 



Figure 15. Drag and moment coefficients versus ring 
length; 2.36-in. rocket. 


ring tail that would provide the required stability. 
The ring tails considered were of two types : One had 
streamlined leading and trailing edges on the ring as 
well as streamlined propellent nozzles, while the other 
was made of commercial grade stampings and chan- 
nel shapes. A series of tests was also run to determine 
the effect of the length of the ring on performance. 



Figure 16. Variation in length of ring tails; 2.36-in. 
rocket. 


In Figure 15 are given the drag and moment co- 
efficients for a series of rings varying in length from 
P/ie to 2 ^ in. or from 0.45 to 1 caliber. There is a 
very rapid increase in moment as the ring length in- 
creases from 0.45 caliber until the maximum stabiliz- 


ing moment is reached at a ring length of 0.8 caliber. 
The drag decreases only about 5 percent as the length 
of the ring is reduced from 1.0 to 0.45 caliber. Figure 
16 is a photograph of the model showing the varia- 
tions in the length of the ring tails in this series. 

Of all the ring tails tested, the three types of con- 
struction that gave the highest stabilizing moment 
are those shown in Figure 17. Descriptions of their 


?■ 



Figure 17. Rocket (2.36-in.). Three types of construc- 
tion giving high stabilizing moments. (A) Tail No. 21, 
(B) tail No. 35 (construction identical to No. 32 but 
shroud ring length = 0.51 caliber), (C) tail No. 47 (con- 
struction identical to No. 48 but shroud ring length = 
1.19 calibers). 


construction differences, as well as the results of the 
tests, are shown in Table 2. Note that tail No. 21 as 
tested is identical to the photograph of Figure 17A. 
Tails No. 32 and 48 as tested are the same as shown 


Table 2. Force and moment coefficients for 2.36-in. 
rocket with three good ring tails and original fixed-fin 
tail. 


Tail 

description 

Ring 

length 

in 

calibers 

Drag 
coeffi- 
cient 
Cd at 
0° yaw 

Cross 
force co- 
efficient 
C c Sit 

4° yaw 

IVIoment 

coeffi- 

cient 

Cjif at 

4° yaw 

No. 21 

1 

0.17 

0.19 

-0.013 

Streamlined 
nozzle, ring 
and vanes 

No. 32 

0.82 

0.37 

0.19 

-0.034 

Plain ring, channel- 
shaped vanes and 
stepped nozzle 

No. 48 

0.82 

0.22 

0.22 

-0.048 

Plain ring, channel- 
shaped vanes, and 
plain boom nozzle 
Original fixed fin 


0.30 

0.16 

-0.004 



60-MM MORTAR PROJECTILE 


237 


in Figures 17B and C except that the length of the 
shroud ring was 0.82 caliber for each. 

Only one of the above ring tails has a higher drag 
than the original fixed-fin tail, and two of them have 
considerably less drag. There is not much change in 
the cross force but the increase in moment due to the 
ring tails is very great, varying from three to twelve 
times that of the original tail. Comparing Table 2 
with Table 1, it is seen that the drag, in general, is 
considerably less for the ring tails than for the collap- 
sible-fin tails, and the stabilizing moment is of about 
the same order. 




Figure 18. Mortar projectile (60 mm) with plain and 
notched disk behind tails. 


60-MM MORTAR PROJECTILE 

Although the 60-mm mortar projectile^^ is not 
properly a rocket, it is somewhat similar in design 
and performance and a brief description of it is there- 
fore included here. An outline drawing of the mortar 
is shown in Figure 1, and a photograph is shown in 
Figure 2 of Chapter 9. This projectile is fired by drop- 
ping it into the mortar tube. When it strikes the bot- 
tom of the mortar, a cartridge in the aft end of the 
projectile is ignited, thus projecting the missile. 
Greater velocity and range are obtained by attaching 
wafers of powder to spring clips provided on the tail 
fins. 

The following physical data pertain to this pro- 
jectile: 


Diameter 

2.362 

in. = 1 caliber 

Overall length 

9.54 

in. = 4-f- calibers 

Distance, nose to CG 

0.49 

X length 

Weight as fired 

2.90 

lb 

Velocity, cartridge only 

225 

fps 

Range at 45°, cartridge only 

488 

yd 

Velocity, cartridge plus 4 
wafers 

518 

fps 

Range at 45°, cartridge plus 

4 wafers 

1,984 

yd 


Figure 3 in Chapter 9 shows the force coefficients 
with the fin tail mounted on booms of various lengths. 
The material increase in stability which can be ob- 
tained by using a boom with a fin or ring tail is very 
apparent in this case. 

It was thought that the extended boom might be 



Figure 19. Drag and moment coefficients; 60-mm 
mortar projectile. Fin tail with disks. 




rinirvim T 


238 


NONROTATING PROJECTILES WITH STABILIZING SURFACES 


objectionable, so other means for increasing stability 
were sought. The installation of a disk immediately 
aft of the fins proved to be quite effective. While this 
illustrates the fact that, in many cases, the stabilizing 
moment can be increased by increasing the drag, it 
should be noted that the large gains obtained here are 



Figure 20. Mortar projectile (60 mm) . Flow line draw- 
ing for original tail design. 


not due to drag alone but to an added cross force as 
well. Figure 18 shows the model with a plain and a 



Figure 21. Mortar projectile (60 mm). Notched disk 
behind tail. 


notched disk, both of which greatly increased sta- 
bility. In Figure 19 are given the force coefficient 
curves for this projectile with the original fin tail, also 
with the addition of plain disks 0.56 and 0.75 caliber 
in diameter, as well as a notched disk. From these 
curves it is seen that at small yaw angles the disk 
0.75 caliber in diameter increases the drag about 120 
per cent while the moment coefficient is increased 700 
per cent. The corresponding figures for the 0.56-cali- 
ber disk are 75 and 330 per cent. 

The flow line drawings of this projectile show very 
clearly the effect of the added disks. Figure 20 is the 
flow line drawing of the prototype in which is seen 
the typical disturbance in the wake of the blunt 
boom on which the fins are mounted. The great in- 
crease in disturbance caused by the disks is indicated 
in Figures 21 and 22, showing the 0.56-caliber and 
notched disks. This added disturbance caused by the 
disks is consistent with the observed increase in drag. 



Figure 22. IVIortar projectile (60 mm) with 0.56-cal- 
iber disk behind tail. 


I 


i CO-MlDL^'ITri ? 


Chapter 15 

SPIN-STABILIZED ROCKETS 


15 1 GENERAL FEATURES 

OF SPINNER ROCKETS 

T wo DISTINCT MEANS are used to give stability to a 
rocket. In one case fins, or other stabilizing sur- 
faces, are attached to the outside of the rocket body 
or else mounted on a boom aft of the body; in the 
other no stabilizing surfaces are used, the stability 
being achieved solely by the spinning of the rocket as 
with a rifle bullet. With spin-stabilized rockets the 
spin is imparted to the projectile by setting the pro- 
pellant nozzles at a definite angle with its axis. 
When stabilizing fins are used, the propellant is 
generally discharged through a single axial nozzle. As 
a rule, spin-stabilized rockets operate at velocities 
ranging from a little below sonic (700 or 800 fps) to 
1,500 fps or more. 

With increasing velocity, drag has an increasing 
effect on the range of a projectile. Consequently, it is 
important to reduce the drag by maintaining as 
smooth a body shape with as few projecting surfaces 
as possible. This is particularly true for velocities 
near sonic where compressibility effects become im- 
portant. In these cases spin stabilization with the 
elimination of tail surfaces is advantageous. 


Effects of Propellant 
Burning 

It is easily seen that as the propellant is used up, 
the rocket weight and center of gravity location are 
changed with a resultant change in its behavior dur- 
ing flight. This must be taken into account in design- 
ing the projectile and some effort has been made to 
reduce the effects of propellant consumption to a 
minimum as in the case of the 15-cm German 
spinner shown in Figure 5. With this rocket the pro- 
pellant nozzles are located around the offset in the 
body, ahead of the main charge. In general the pro- 
pellant burning time is of the order of 1 sec. Any 
effect on stability due to changing weight or shifting 
of the center of gravity CG or any effects on the yaw 
and lateral displacement due to malalignment of 
nozzles will be felt during this accelerating peri- 
od. If the propellant is consumed before the rocket 


has left the launcher, these effects will be largely 
eliminated. 

15.1.2 Applicability of Water Tunnel Tests 

Water tunnel tests are valid for air-flight pro- 
jectiles operating at velocities in the range where the 
air may be assumed to be incompressible. This range 
extends to about 750 fps or somewhat below sonic 
velocity. As spin-stabilized rockets generally have 
velocities greater than this, the water tunnel tests 
will apply directly only to the portion of the ac- 
celerating period below a velocity of 750 fps. This 
accelerating period is quite important in determining 
the performance of the projectile during its subse- 
quent flight because the dispersion of the projectile 
is dependent on the type of oscillatory motion set up 
initially. Water tunnel data can be used to calculate 
the period of oscillation of a projectile in subsonic 
flight as well as the maximum lateral displacement 
during an oscillation. 

15.1.3 Hydrodynamic Characteristics 

Spin-stabilized rockets are usually plain bullet- 
shaped bodies with ogival noses and blunt ends. The 
hydrodynamic forces on such bodies are discussed in 
Chapter 8 and generalized conclusions are given 
there. The salient features of drag, cross force, and 
moment are summarized briefly as follows : 

1. The drag coefficient for a wide variety of bullet- 
shaped bodies has a moderate value in the neighbor- 
hood of 0.25. 

2. The cross force coefficient increases approxi- 
mately linearly with yaw. 

3. The moment about the center of gravity is gen- 
erally destabilizing, although on some projectiles, de- 
pending on the nose and afterbody shapes, there may 
be a slight stabilizing moment for yaws of about 1° or 
less. 

The latter result is important since, if the rocket is 
spin-stabilized, it is desirable to eliminate this slight 
stability near zero yaw. Tests of modifications of 
specific rockets showed that this can be accomplished 
by changing the type of nose or by streamlining the 
afterbody. 


239 


240 


SPIN-STABILIZED ROCKETS 




15 CM GERMAN SPINNER ROCKET 



^ M i U-M-lirf l-M U -M bJ ■! 

0 5 10 15 20 25 

SCALE, INCHES 

Figure 1. Outline drawings of spin-stabilized rockets. 


15 2 REVIEW OF SPECIFIC TESTS 

The rockets investigated included the 3.5-in. ro- 
tating rocket; the 4.5-in. T38E3 rocket; the 5-in. SSR 
rotating rocket, and the 15-cm German spinner 
rocket. Outline drawings of these are shown in Fig- 
ure 1. A review of their specific characteristics fol- 
lows. 


Figure 2 is a photograph of this rocket and Figure 3 
shows several types of afterbodies that were tested. 
The extent to which slight streamlining of the after- 
body is effective in reducing stability near zero yaw is 
shown in the moment coefficient curves of Figure 4. 
It has been found that the type of nose on bullet- 
shaped projectiles also affects the stability. A rather 


^ ^ 3.5-in. Rotating Rocket 

This rocket®®’®! has the following physical char- 
acteristics (without propellant) : 



Figure 2. SSR rocket (3.5-in.). 


Diameter 
Overall length 
Distance, nose to CG 
Rotation 

Transverse moment of inertia 
Transverse radius of gyration 
Polar moment of inertia 
Polar radius of gyration 
Weight in flight 
Velocity 


3.5 in. = 1 caliber 

24.87 in. = 74- calibers 

0.443 X length 
181 rps 

7.25 lb-ft2 
0.576 ft 
0.285 lb-ft2 
0.117 ft 

21.75 lb 

760 fps 


blunt tapering nose will produce a slight stabilizing 
moment at very small yaw angles and this can be 
eliminated by changing to a long-radius ogive nose, 
although changing the type of nose is not as effective 
as streamlining the afterbody. 

Tests were made to determine to what extent 
asymmetry of the nose might affect performance. 


l. u)MH)l:\TnO 


REVIEW OE SPECIFIC TESTS 


241 






•«a69p|a98" 
— 1.73" H 

AFTERBODY 54 


fn 

L 




I 

I 


0.69" .H- 


1.73 


AFTERBODY 55 


a9s 

—A- 

1 y 

'■ F< 

1 / 
j 

\ 

1 


2.17" - 



Afterbody 56 afterbody 57 

Figure 3. Afterbodies for 3.5-in. SSR rocket. 


ai4" 


I 

I 




1.62 •* 


afterbody 89 


The axis of the nose was deliberately offset so the tip 
of the nose was displaced a little over 3^ in. from its 
true position. In other words, the axis of the nose 
made an angle of 134° with the axis of the body. The 
force tests showed that this amount of asymmetry of 
the prototype nose would not cause a significant 
change in the fluid forces on the rocket. The effect of 
this asymmetry in setting up oscillations due to 
rotational unbalance would probably be much more 
severe. 

15 2.2 15 -cm German Spinner Rocket 

The physical data for this rocket are as follows:®^ 


Maximum diameter 

6.17 

in. ( = 15cm) = 1 caliber 

Overall length 

36.18 

in. = 5.85 calibers 

Weight with propellant 75.3 

± 2 1b 

Weight without 



propellant 

61.0 

± 2 1b 

Distance, nose to CG 

21.5 

in. (= 0.595 X length) 

Axial moment of inertia 

0.0625 slug-ft2 

Transverse moment of 



inertia 

1.06 

slug-ft2 

Jets from aft end 

10.48 

in. = 1.7 calibers 

Velocity 

Supersonic 


This rocket is a bullet-shaped projectile of novel 
design although its performance is similar to other 
spin-stabilized rockets. Figure 5 is a photograph of 
the model and Figure 6 shows its moment and force 
coefficients. While this rocket does not have a stabi- 
lizing moment for small yaw angles, the destabilizing 
moment from zero to 1 degree yaw is very small. 

It is of interest to note that the performance 
characteristics shown in Figure 6 are roughly similar 
to those that have been measured for simple cylin- 
drical projectiles with either ogival or hemispherical 
noses and square trailing ends. For example, a cylin- 


der with hemispherical nose 6 calibers long (note that 
the spinner rocket is 5.85 calibers long) has a drag 
coefficient of 0.275 at zero yaw, and increases to 0.40 
at 8 degrees. Corresponding figures for the 15-cm 
spinner are 0.23 and 0.33. The reason for this similar- 



Figure 4. Moment coefficients for afterbodies shown 
in Figure 3; 3.5-in. SSR rocket. 


^)’SIIi7i:m I 


242 


SPIN-STABILIZED ROCKETS 


ity is that both the present spinner rocket and the 
simpler “bullets’’ have the same general cylindrical 
shape with rounded nose and blunt trailing end. As 
the velocity of sound is approached or exceeded, 
these statements no longer apply since nose shape 
then becomes of paramount importance. It can be 
said, as a first approximation, that for simple bullet- 
shaped bodies traveling at subsonic speeds, the after- 
body and tail shapes largely determine the aerody- 
namic forces, whereas for supersonic speeds, the nose 
shape is the predominating influence. 

An interesting indirect measure of the deviation 
of the subsonic characteristics from those at super- 
sonic velocities can be obtained by making use of the 



Figure 5. German spinner rocket (15-cm). 


spinning stability criterion and the propulsive nozzle 
alignment angle. 

According to Hayes,®^ the condition for stable mo- 
tion of a spinning projectile is 


or 


where A 
N 
B 




4' 


AW2 , 


( 1 ) 




AD Cm a 1 


axial moment of inertia in slug-feet^, 
spin in radians per second, 
transverse moment of inertia in slug- 
feet^, 

moment factor in foot-pounds per radian 
of yaw. 


M 

4^ 


a 


M A 


yaw in radians. 


For projectiles spun by rocket jets, the stability re- 
quirement can be written in terms of the angle which 
the jet centerline makes with the projectile axis. This 
is accomplished as follows : the relation between im- 
pulse of the jets and the resulting linear and angular 
momentums can be written 


{F cos 6)t = mv, 

Tt = (F sin e)rt = AN, 

or eliminating t between the two expressions 
,, 'invr tan 6 


(2) 


where v = maximum velocity reached by rocket in 
feet per second, 

F = jet reaction in pounds, 
t = burning time of propellant in seconds, 
m = mass of projectile in slugs, 

T = torque exerted by jets about projectile 
axis in pound-feet, 

r = radius to centerline of jet ring in feet, 

B = jet alignment angle. 

If the value for the spin velocity N given by this 
equation is substituted in the stability relation (1) 
above and the resulting relation rearranged, the fol- 
lowing expression for the required jet angle is ob- 
tained : 

In this equation B and Cm 14^ are the variables, 
all other quantities being constant for a given pro- 
jectile. If values of Cm/4^ from the water tunnel tests 
are used to evaluate B, an angle of approximately 6° 
is obtained as the minimum jet angle for stability at 
subsonic velocities. Since, as equation (2) shows, N 
varies directly with tan B, the actual nozzle angle of 



Figure 6. Force and moment coefficients; 15-cm Ger- 
man spinner rocket. 


14° means that the stability coefficient has 

a value of about 5.63 instead of the minimum of 1. 
Although a part of this large excess is undoubtedly 
needed to provide the desired “stiffness” to the Ger- 
man spinner rocket, it is probable that this high value 
indicates that, at supersonic velocities, the destabi- 
lizing aerodynamic moment coefficient is consider- 
ably greater than it is at subsonic speeds. 


2 ^ 4.5-Inch HE Rocket, T38E3 

This is another example of a bullet-shaped body 
that has a small stabilizing moment at small yaw 
angles. The general outline of the projectile®^ is shown 



REVIEW OF SPECIFIC TESTS 


243 


in Figure 1, and Figure 7 is a photograph of the 
model. The following physical data apply to this 


rocket : 

Maximum diameter 
Overall length 
Distance, nose to CG 
Weight without propellant 
Velocity 


4.515 in. = 1 caliber 
31.44 in. = 7— calibers 
0.515 X length 
42.5 lb 
830 fps 


In Figure 8 are given curves for the drag, cross 
force, and moment coefficients up to a yaw angle of 



Figure 7. HE rocket, T38E3 (4.5-in.). 



Figure 8. Force and moment coefficients; 4.5-in. HE 
rocket, T38E3. 

10°. The drag coefficient for zero yaw is a little less 
than 0.25, which appears to be the value common to 
most projectiles of this type. 

15 2.4 5 -Inch SSR Rotating Rocket 

Four models of this rocket®^ were tested. Figure 1 
gives the outline drawing of model 32 and Figure 9 
shows photographs of models 20 and 32, the principal 
differences between the various models is in the over- 
all length and the type of nose. Table 1 gives data 
pertaining to these four models. 

In Figure 10 are plotted the cross force, drag, and 
moment coefficients for models 20 and 32. These 


Table 1. Physical characteristics of the 5-in. SSR 
rotating rocket. 


Model 

Max 
diameter 
in in. 

Overall 
length 
in in. 

Weight 
loaded 
in lb 

Weight 
in flight 
in lb 

Velocity 
in fps 

No. 20 

5 

28.9 

49.7 

39.6 

1,500 

No. 32 

5 

31.6 

51.4 

41.3 

1,500 

No. 25 

5 

31.7 

49.9 

44.3 

800 

No. 21 

5 

31.7 

48.3 

42.7 

800 


models also show drag coefficients of 0.25 or less 
corresponding to other projectiles of this type. Two 
tests were made to determine the variation in drag 
with Reynolds number, the results of which are 
shown in Figure 11. By extrapolating the curves for 



Figure 9. Five-inch SSR rotating rocket, models 20 
and 32. 




Figure 10. Force and moment coefficients. Five-inch 
SSR rocket, models 20 and 32. 


CC OM'IDKN'n Vl L 



244 


SPIN-STABILIZED ROCKETS 


a4 


oa3 

o 














R FOR i 
800 FT/SE^ 15 

WTOTYPEI 
00 FT/SEC 





MODEL i 

|.U 







n 

1 

1 



r 

1 

1 

1 



r-y* 

— o- 

r 










MODEL 

\ 

o 

CM 








i 


S2 a2 
It 


ai 


7xl0» 10® 


3 4 5 6 7 8 9 10^ 

REYNOLDS NUMBER, R 


Figure 11. Drag versus Reynolds number; 5-in. SSR rocket, models 20 and 32. 




Figure 12. Flow line drawings; 5-in. SSR rocket at 0 
and 10 degrees yaw. 


the model to the Reynolds number of the prototype, 
it is found that the drag coefficient for the prototype 
will be between 0.21 and 0.23. Note that this applies 
only so long as velocity of flight is below the sonic 
velocity. 

By observing the model in the polarized light 
flume, it is possible to prepare a flow line drawing 
showing the flow about the model. Figure 12 is a 
flow line drawing of one of the models showing clearly 
that there is little or no disturbance along the surface 
of the body. There is the typical disturbed flow in the 
wake of the end of the model that is always found 
with blunt afterbodies. 


Chapter 16 

DEPTH CHARGES 


6 1 GENERAL DISCUSSION 

A DEPTH BOMB Can be considered as a member of 
the family of projectiles which also includes air 
bombs and torpedoes. All are explosive-containing 
objects which may be launched by aircraft, even 
though other means are also used. Differences stem, 
primarily, from the location of the area each is de- 
signed to strike. The ordinary air bomb is intended 
to strike the upper areas of targets at or near the sur- 
face of the earth or water. The torpedo is used to 
attack vulnerable areas of vessels at a point under, 
but not far under, the water surface. Depth bombs 
are for use in the general zone from just under the 
water surface to any desired depth. In consequence, 
the air bombs will have little or no underwater tra- 
jectory; that of the torpedoes will be primarily hori- 
zontal, while that of the depth bombs will be mainly 
vertical. A means of self-propulsion is essential only 
in the case of the torpedo with horizontal trajectory. 
High average and terminal velocities are desirable for 
depth bombs but the evasive action of their targets is 
relatively slow and, hence, it is less important than 
the speed of torpedoes which must hit targets that 
can maneuver much more rapidly than submerged 
submarines. The relatively low velocities and greater 
course depths of the depth bombs also make consid- 
eration of cavitation less important and do not 
necessitate extreme streamlining. Furthermore, high- 
ly streamlined forms tend toward static instability 
which is desirable in torpedoes with their special con- 
trol devices but is objectionable in depth bombs. 
Trajectories must be predictable, reliable, and ob- 
tainable from the stability inherent in such pro- 
jectiles. There are other similarities and differences 
but those mentioned illustrate the general relation- 
ships within this family. 


16 2 METHODS OF LAUNCHING 

Depth bombs are ordinarily launched either by 
dropping from aircraft in flight over the target or by 
being shot from a suitable device on a water-sup- 
ported vessel. Each of these methods has some in- 
fluence on the design of the bomb. 


163 DESIGN REQUIREMENTS 

Many factors are involved in the design of a depth 
bomb. Generally, the starting point will be a definite 
kind and amount of explosive based upon tactical 
considerations. This determines a tentative minimum 
volume which must be shaped, spacially, to a suitable 
length-diameter relationship. These dimensions may 
be subject to restrictions due to previously existing 
apparatus to be associated with their use, such as the 
launching or projection devices, as well as to hydro- 
dynamic considerations, such as drag and stability. 
Further evolution of the design includes requirements 
of structural strength, such as wall thickness; of func- 
tional parts, such as fuzes ; of manufacturing, such as 
simplicity of construction; and of handling and 
storage. There is, finally, the overall requirement 
that the explosive charge will reach the vicinity of its 
target with an acceptable minimum of dispersion. It 
is known that improvement may be had in this re- 
spect if lateral travel, introduced when the projectile 
is ejected, be checked upon water entry. This can be 
obtained by a nose shape which will produce a large 
entrance bubble. 

16.4 USEFULNESS 

OF HYDRODYNAMIC TESTS 

Hydrodynamic tests are of great usefulness in de- 
termining the actual characteristics of the prototype. 
They permit prediction of full-scale performance to 
reasonable degrees of accuracy, and detailed study of 
the various factors involved is greatly simplified and 
facilitated. Cavitation phenomena may be photo- 
graphed if desired. Changes which may be suggested 
by the results of such tests may be incorporated 
readily and tested anew. 

16 5 SPECIFIC DEPTH BOMBS TESTED 

The depth bombs tested by this laboratory in- 
cluded those known as the New London and New 
London Modified; the 7-in. diameter depth charge, 
also referred to as the X-42; the Mousetrap and 
Mousetrap Modified ; the AN Mark 41 ; the AN Mark 
53; and the British Squid. 


C ^(>SK»)kNrRlr) 


245 


246 


DEPTH CHARGES 


Figure 1 shows photographs of the projectile mod- 
els listed above, and Figure 2 shows their outlines, all 
of which are to the same scale for the group. The ex- 
plosive charge weights and other physical character- 
istics for these projectiles are given in Table 1. 

Small-Charge Group 

Figure 3 is a composite graph of yaw angle*" tests 
for five of the depth charges tested early in the pro- 
gram. The data for this group were not corrected for 
support interference effects. There are three sets of 
curves in this figure. The group at the top is for 
center-of-pressure distance against yaw angle. The 
difference between the center-of-pressure distance 
and the center-of-gravity distance may be used to 
indicate the degree of static stability instead of 
curves of moment coefficient about center of gravity. 
The ordinate scale is the ratio of X divided by L, 
where L is the length of the projectile, and X is the 
distance of the center of pressure from the nose. It 
may be seen that the Mousetrap projectiles had the 

^ Definition of term and symbols are given in Appendix. 


highest ratio, with the original Mousetrap having 
the greater of the two. Both of these results might 
have been anticipated. Boom tails give greater static 


Table 1. Physical characteristics of depth bombs tested. 


Projectile 

Diam- 

eter 

in 

in. 

Over- 

all 

length 
in in. 

Weight 
of ex- 
plosive 
in lb 

Total CG distance 
weight from nose di- 
in vided by over- 
lb all length 

New London 

6.0 

40.0 

30 


Mousetrap 

7.2 

35.75 

30 

about 0.295 

60 

7-in. diam- 

7.0 

38.5 

40 

70.94 0.310 

eter bomb 

Modified 

7.2 

35.5 

30 

0.347 (approx) 

Mousetrap 

Modified 

6.0 

50.75 

40 

80 0.315 

New 

liondon 

AN Mark 41 

15.0 

52.0 

227 

330 0.317from nose 

fuze 

0.297 

British Squid 

11.75 

55.0 

198 

386.4 0.364— air 

0.335 — sea 

water 

AN Mark 53 

13.5 

52.5 

225.46 

323.8 0.375 from nose 
fuze 

0.355 





Figure 1. Photographs of specific depth charges tested. A-J inch 


SPECIFIC DEPTH BOMBS TESTED 


247 


NEW LONDON 


C 

^ 

7 IN. DIAM DEPTH CHARGE 



^ 


( 


MOUSETRAP 




MODIFIED NEW LONDON 





-A- 




MK 53 


IT 




— rr^ 


L— ^ 





SCALE, INCHES 

Figure 2. Depth charge group. Outline drawings. 


rCOM’IOKN I KI ZA 


248 


DEPTH CHARGES 


stability and so does bluntness of nose as compared 
with less blunt noses, other things being equal. How- 
ever, the decrease in static stability in the case of the 
Modified Mousetrap was relatively immaterial and 
the reduction in the drag coefficient from the highest 
to the lowest in the group, as shown in the middle set 
of curves, was much more important. The New Lon- 
don types, particularly the Modified New London, 
had the least static stability. Their shape approaches 
that of the torpedo which should have little or no 
static stability, since it must be amenable to the ac- 



YAW ANGLE, DEGREES 

Figure 3. Effect of yaw on Cd, Cc, and X /L for group 

of small charge depth bombs. 

tion of control devices. The higher stability of the 7- 
in. diameter depth charge, of the same general shape 
as the New London projectiles, is presumably due to 
its blunter nose. 

The drag coefficient curves are also consistent with 
experience. Very blunt noses have, in themselves, a 
high degree of drag. The Mousetrap with the bluntest 
nose gave the highest readings. The Modified Mouse- 
trap gave the lowest because the gain from its nose 
shape, which was like that of the 7-in. diameter depth 
charge and less fine than the New London noses, was 
not offset by the skin friction drag due to greater 
wetted surface in these other projectiles. 

The cross force coefficient curves have zero value at 


zero yaw angle and vary practically linearly with 
yaw. 

16.5.2 

Figure 4 shows the effect of yaw angles on Cd, Cc, 
and Cm for the AN Mark 41 Bomb®® and various 
modifications which further illustrate the effect of 
various projectile components on these coefficients. 



Figure 4. Effect of yaw on Cd, Cc, and Cm for the AN 
Mark 41 bomb and modifications. 


These data are also uncorrected for support inter- 
ference. The top curve in the top group is the drag 
coefficient for the standard (or original) design model 
at yaw angles to + 10 degrees. An unusual dip may be 
seen to occur between approximately S }/2 and 4 de- 
grees. This appears to be a characteristic associated 
with this particular prototype nose and the sharp 
reduction in the drag coefficient is presumably due to 
a change in flow conditions over that yaw angle range. 



SPECIFIC DEPTH BOMBS TESTED 


249 


The drag coefficient was markedly reduced by the 
substitution of the new afterbody and tail, shown in 
Figure IH. The stripping of body protrusions did not 
contribute any of this reduction as the flow separa- 
tion from this nose caused the high-velocity water to 
flow in a region beyond their effective extension from 
the body as may be seen in Figure 5. The dip in the 
drag curve still appears although shifted toward 
zero yaw by 13^ degrees. The long-dash curve shows 
the results obtained by merely substituting a some- 
what smoother nose on the prototype. The reduction 
of Cz) at 0-degree yaw was about 41 per cent, and its 
rate of increase with yaw angle was smoothed out 
and reduced. Separation of flow at the nose was also 



Figure 5. AN Mark 41 prototype. Flow line diagram 
for (A) 0- and (B) 10-degree yaw angles. 


reduced and high-velocity water was close enough to 
the body surface to strike protrusions, as shown in 
Figure 6. When they were removed, an additional 
reduction of drag coefficient resulted so that, at 0- 
degree yaw, the total reduction was 4734 per cent of 
the original total Cd- The one long-two short-dash 
curve shows the results with the Squid nose, stripped 
body, and new afterbody and tail with a reduction 
at zero yaw of 59 per cent. Such a reduction would 
increase the terminal velocity in water from 15 to 23 
fps, approximately. It is probable that a still further 
reduction of 10 per cent or better could be obtained 
in Cz) merely by rounding all the leading edges of the 
fins and shroud ring of the tail. 

The cross force coefficient was affected only slightly 
by any of the changes made. All curves were on or 
within the limits shown in the group which extends 


from zero to the upper right of the graph. The sub- 
stitution of a finer nose increased the cross force co- 
efficient as it normally does in the absence of other 
factors. 

All moment coefficient curves indicate static sta- 
bility, the degree increasing with the size of the angle 
the curve makes with the horizontal axis. Thus, it 
may be seen that the model with the new nose, 
stripped body, new afterbody, and tail had the great- 
est static stability, and the prototype with new nose 
had the least of the group. The prototype itself 
shows a radical change between 334 and 4 degrees of 
yaw similar to that observed in the drag curve. This 
indicates a condition of uncertainty of action in this 
region, which is somewhat objectionable. 



Figure 6. AN Mark 41 with new nose. Flow line dia- 
grams for (A) 0- and (B) 10-degree yaw angles. 


® ' British Squid 

Figure 7 shows the influence of yaw angle on Cz?, 
Cc, and Cm for the British Squid with five different 
noses.®^"^® All these noses except the No. 131 were 
truncated spherogives with different flat areas. In all 
cases the overall length and maximum diameter were 
the same. The noses, designated in the laboratory by 
Nos. 42, 45, and 46 were ogives with a radius of 12.5 in. 
and a constant horizontal length of 5.77 in. The 
center of the ogive was shifted to give flat areas on 
the front of the nose of 7.90, 8.93, and 9.95 in. diam- 
eter, respectively. The prototype nose is shown in 
Figure IJ. It is similar to those described immedi- 
ately above except that the flat area had a diameter 
of 8.75 in. and there was a bourrelet on the nose im- 




250 


DEPTH CHARGES 


mediately before its junction with the body. This 
nose, together with the No. 45 nose and a special 
nose, laboratory designation No. 131, maybe seen in 
outline in Figure 3, Chapter 9. The contour of the 
No. 131 nose is based on the formula 

where x is measured along the axis from the base of 
the nose and y is the distance from the axis to the 
nose surface. 



Figure 7. Effect of yaw on Cd, Cc, and Cm for the 
British Squid with several noses. 


The Cd curves for the Nos. 46, 45, and 42 noses 
show the progressive reductions due to reducing the 
size of the flat leading face or, in other words, of re- 
ducing nose bluntness in this manner. The prototype 
nose is very similar to the No. 45, and the drag co- 
efficient obtained with it would be only slightly under 
that for the No. 45 had all other conditions been 
similar. The additional reduction shown in the graph 
was due to thinner material in the fins and rounded 
leading edges. The curve for the No. 131, or special 


nose, shows the additional reduction from further 
streamlining. This model also had the thin tail with 
rounded leading edges. 



Figure 8. Influence of cavitation parameter on drag 
coefficient for the British Squid depth charge with three 
noses. 



Figure 9. British Squid with No. 45 nose. Flow line 
diagram for 0- and 10-degree yaw angles. 


The curves for the cross force coefficient for the N os. 
45 and 46 noses were identical within limits of meas- 
urement. The No. 42 nose had a higher Cc as is gen- 
eral for less blunt noses, but the finest nose of the 


^NFTDENTIAL rP 


SPECIFIC DEPTH BOMBS TESTED 


251 


group had a smaller value which is an anomaly 
unless attributable to the slight differences in tail 
structure. 

The moment coefficient curves indicate static 
stability for all models, that for the prototype with 
special nose having the highest. 



K = 0.25 


Figure 10. British Squid. Cavitation: /^ = 0.45, 0.35, 
0.25. Upper view in each set is for prototype. Lower view 
is for prototype with special nose, (A)-(F) inch 


Figure 9 shows the flow line diagrams for the Squid 
with original nose for zero and 10 degrees of yaw. 
Separation on the nose and afterbody is apparent. 

Figure 10 shows cavitation with the prototype 
Squid and prototype with the special nose described 
above. The complete prototype is the upper view in 
each set. Values of K were 0.45, 0.35, and 0.25. These 



0 2 4 6 8 10 


YAW ANGLE, DEGREES 

Figure 11. Effect of yaw on Cd, Cc, and Cm for the 
AN Mark 53 bomb. 

photographs show clearly the greater cavitating 
tendency of the prototype nose. 


Figure 8 shows the effect of cavitation parameter 
K on the drag coefficient for the Squid with Nos. 42, 
45, and 46 noses. There is a slight progressive decrease 
in Cd as the K value is lowered, until and after incipient 
cavitation is established. When the cavitation ‘‘col- 
lar” has a width of about 34 in. on the model, the 
drag coefficient increases sharply and continues this 
trend with further reduction of K values. 


16.5.4 53 

Figure 11 shows the drag, cross force, and moment 
coefficients for positive yaw angles to 10 degrees for 
the AN Mark 53 bomb to the same scale as used for 
the AN Mark 41, Figure 4. The relatively high drag 
coefficient (0.42) is due, primarily, to the blunt nose 
shape. The cross force coefficient is a linear function 


252 


DEPTH CHARGES 


of the yaw within the test range and is comparable to 
that of the AN Mark 41. The moment coefficient 
about the center of gravity is also comparable and 
shows a greater slope between 0 and 2 degrees than 
between 2 and 10 degrees. 


The pressure distribution was measured on this 
projectile in order to determine a suitable place for 
the hydrostatic fuze connection and for cavitation 
characteristics. Details of these findings may be 
obtained from the report.'^^ 


Chapter 17 

AIR BOMBS 


171 INTRODUCTION 

T he term “air bombs,” as here used, refers to pro- 
jectiles whose trajectory is wholly in air. As dis- 
tinguished from rockets, they contain no propellant, 
the initial trajectory conditions being determined 
wholly by the magnitude and direction of the launch- 
ing velocity. They are distinguished from projectiles 
such as depth charges and aerial torpedoes whose 
trajectory is wholly or partly in water by the follow- 
ing characteristics: 

1. They have many times the density of the fluid 
medium and in consequence the damping forces are 
low. Air bombs, therefore, require large stabilizing 
fins not only for static stability but also to supply the 
damping necessary for dynamic stability. 

2. A higher drag usually is permissible since high 
terminal velocities are seldom important. 

3. Cavitation does not occur, but extending lugs, 
fuzes, and other irregularities may induce supersonic 
effects before the bomb as a whole attains sonic 
velocity. 


17 2 REVIEW OF TEST RESULTS 
17.2.1 Bombs Tested and Scope of Tests 

The following air bombs have been investigated by 
model test in the water tunnel of the Hydrody- 
namics Laboratory :72 

1. The 100-lb concrete practice bombs, with three 
designs of stabilizing fins. 

2. The M38A2 100-lb practice bomb. 

3. The AN-M43 GP 500-lb bomb. 

4. The AN-M56 LC 4,000-lb bomb. 

Figure 1 shows outline drawings of the above 
bombs, all to the same scale. Figures 2 to 7 are photo- 
graphs of the models, and Table 1 gives the principal 
dimensions. 

All the bomb bodies are of the same type, with 
cylindrical midsections, ogival noses either rounded 
or blunt at the tip, and afterbodies in the form of 
truncated cones. 

All the stabilizing tails are of the square box type 
with fins extending outward from the box corners, 


except for one of the concrete practice bombs, which 
has a drum-type or shroud-ring tail. 

The water tunnel models were accurate reproduc- 
tions of the prototype except that the arming fuzes 
were omitted. The tests were made under steady- 
state conditions and the results gave the hydrody- 
namic forces and moments for steady-state conditions 
only. No tests were conducted to determine the 
damping forces on the bombs when oscillating in free 
flight or fall. 

17.2.2 Force and Moment Coefficients 

Figure 8 shows the force and moment coefficients 
determined by tests of the model of the AN-M43 
GP 500-lb bomb. The general shape of the coefficient 
curves is characteristic of all the models tested. For 
comparison the principal hydrodynamic character- 
istics of all the bombs, as determined from the model 
tests, are given in Table 2. Definitions of terms and 
symbols used in both Figure 8 and Table 2 are given 
in the Appendix. 

The drag coefficient of the air bombs investigated is 
more than double that of more fully streamlined 
shapes, such as torpedoes and certain types of depth 
bombs having dimensions of the same order of mag- 
nitude and approximately the same surface areas. 

For air bombs whose density is many times that of 
air, a sufficient condition for dynamic stability is that 
the resultant of the steady-state hydrodynamic forces 
should fall aft of the center of gravity of the pro- 
jectile.7^ For all of the bombs investigated this con- 
dition was satisfied. However, the magnitude and 
frequency of the damped oscillation following a 
perturbation cannot be determined without knowl- 
edge of the damping forces. 

^ * Effect of Asymmetry 

None of the bombs has complete structural sym- 
metry about its longitudinal axis, due principally to 
the manner of construction and assembly of the tails. 
The result of asymmetry, particularly in the fins, is 
to produce a rudder effect in flight resulting in devi- 
ations from the trajectory of a truly symmetrical 
projectile. The effect of asymmetry on moment and 


^jr nNMDKN im 


253 


254 


AIR BOMBS 







Table 1. Principal prototype dimensions. 



Concrete practice bombs 

Large Small Drum 

box tail box tail tail 

CPCA-1 CPCA-2 CPCA-3 

M38A2 

100-lb 

practice 

bomb 

AN-M43 

GP 

500-lb 

bomb 

AN-M56 

LC 

4,000-lb 

bomb 

Maximum diameter in in. 

8 

8 

8 

8 

14 

34 

Overall length in in. 

38.50 

38.50 

45.50 

47.50 

58.14 

116.08 

Body length in in. 

30.10 

30.10 

30.10 

40.66 

48.33 

96.12 

Afterbody taper in degrees from longitudinal axis 

10.3 

10.3 

10.3 

15.7 

24 

30 

Side of fin box in in. 

6.00 

4.75 

8 (dia) 

6.00 

7.60 

22.56 

Max span of fins in in. 

11.00 

11.00 

8 (dia) 

10.77 

18.94 

47.62 

Weight in lb 

103.25 

103.25 

104 

100 

508 

4,200 

Nose tip to CG in in. 

14.75 

14.75 

15.50 

18.15 

24.00 

49.20 

Scale ratio, prototype to model 

4/1 

4/1 

4/1 

4/1 

7/1 

1/1 


REVIEW OF TEST RESULTS 


255 





Figure 2. CPC A No. 1 tail. Large fin box. 


Figure 3. CPCA No. 2 tail. Small fin box. 




256 


AIR BOMBS 


cross force is illustrated in Figure 8, which shows the 
variation of moment and cross force with yaw as 
actually determined for the model of the AN-M43 
500-lb bomb. Neither the cross force nor the moment 
is zero at zero yaw. At a yaw of about 1 degree, the 
moment is zero, but the cross force has a considerable 
magnitude which acts to deflect the trajectory. The 



consequence of asymmetry is a dispersion which is 
unpredictable. Tests at various orientations of the 
tails with respect to the yaw plane showed varying 
degrees of asymmetry. 



Jg 




Figure 9. CPCA No. 1. Flow line drawings; 0- and 

10-degree yaw. 

The coefficient curves of Figure 8 and the coeffi- 
cient values given in Table 2 are obtained from force 
measurements averaged for 180-degree differences in 
orientation and represent the characteristics of 
symmetrical projectiles. 

^ Conclusions 

The high drag results mainly from separation and 
turbulence on the afterbody. This is illustrated 
clearly by Figures 9 to 12 which are drawings of the 
flow patterns observed in the polarized light flume. ^ 


Figure 8. Effect of asymmetry on force and moment 
coefficients. AN-M43 GP 500-lb bomb. 


^ The polarized light flume and methods of obtaining flow 
diagrams are described in Chapter 2. 


Table 2. Comparison of hydrodynamic characteristics. 


Concrete practice bombs M38A2 AN-M43 AN-M56 

Large Small Drum 100-lb GP LC 

box tail box tail tail practice 500-lb 4,000-lb 

CPCA-1 CPCA-2 CPCA-3 bomb bomb bomb 


Drag coefficient, Cd 

At zero yaw 0.285 

At ±6° yaw 0.315 

Cross force coefficient C c 

Cc per degree, zero to + 1° yaw 0.062 

Cc at 4-6'" yaw 0.450 

Moment coefficient Cm 

Cm per degree, zero to -fl® yaw —0.008 

Cm at -b6° yaw -0.085 

Center-of-pressure eccentricity e at -[-O'" yaw —0.189 

Reynolds number X 10”® 

Model in water at 32 fps 2.4 

Prototype in air at 600 fps 12 


0.250 

0.240 

0.270 

0.220 

0.287 

0.305 

0.290 

0.295 

0.260 

0.325 

0.065 

0.050 

0.055 

0.060 

0.056 

0.460 

0.335 

0.440 

0.380 

0.355 

-0.006 

-0.009 

-0.008 

-0.009 

-0.005 

-0.081 

-0.058 

-0.074 

-0.065 

-0.041 

-0.176 

-0.173 

-0.168 

-0.171 

-0.115 

2.4 

2.8 

2.9 

2.0 

1.7 

12 

14 

14 

18 

35 


REVIEW OF TEST RESULTS 


257 


Comparing Figures 9 and 10, it will be noticed that 
the eddies formed by separation on the afterbody 
practically fill the interior of both the fin box on the 
CPC A No. 1 and the drum tail on CPC A No. 3, con- 



siderably reducing the stabilizing effect. On the 
drum-type tail of Figure 10, even though the drum or 
shroud ring is located farther aft than is the fin box 
of Figure 1 1 , it is less effective except near zero yaw. 
The greater effectiveness of the box tail at larger 
yaws may be attributed to the fins which project 
from the corners of the box to a span greater than the 
projectile diameter and extend into undisturbed 
fluid. 

Note that the water tunnel tests are all for a lower 
range of Reynolds numbers than the prototype 
reaches in air flight. The measured cross force and 
moment coefficients probably apply to the prototype 
conditions without correction, although the drag co- 
efficients may be subject to some scale effect. It is 




Figure 12. M32A2 practice bomb. Flow line draw- 

ings. Afterbody 102 at 0- and 10-degree yaw. 



Figure 11. . AN-M56 LC 4,000-lb bomb. Flow line 
drawings; 0- and 10-degree yaw. Tail fins in upper two 
drawings are oriented parallel and normal to projection 
plane; in lower drawings, fins are inclined 45 degrees to 
plane. 



258 


AIR BOMBS 


estimated that this effect is small because the drag is 
primarily form drag caused by the harmful effect of 
the separation at the afterbody. 

Low dispersion and low drag are both desirable for 
the highest aiming accuracy, particularly with the 
very heavy bombs which may be launched singly. To 
accomplish this, a construction is indicated which is 
completely symmetrical about the longitudinal axis 
and has a streamlined shape to minimize drag. 

There is considerable qualitative evidence to indi- 
cate that the random dispersion which remains after 
aiming errors are accounted for is less than would be 
expected on the basis of the average misalignment of 
the tail structure. There is also qualitative evidence 
to show that most bombs rotate during the air flight. 


probably due to chance asymmetries or to the effect 
of the stiffener angle at the fin tips. The effect of the 
rotation is to average the steering error due to tail 
structure misalignment or body damage and thus 
sensibly reduce the dispersion. It is believed that even 
lower dispersions could be obtained by introducing a 
planned rather than a chance amount of rotation. 

Tests on a variety of models having such charac- 
teristics (see Chapter 9) lead to a suggested bomb 
shape with a rather blunt nose, a very short cylin- 
drical section, if any, and a long tapering afterbody 
with a shroud-ring tail as far aft as practicable. For a 
given volume and maximum diameter, such a shape 
would be perhaps ten to fifteen per cent longer than 
the shapes illustrated in Figure 1. 


Chapter 18 

TWO-DIMENSIONAL BODIES 


18 1 CHARACTERISTICS OF HYDROFOILS 
-THE NACA 4412 SECTION 

^ ^ Scope of Investigation 

T he performance data of most profiles which are 
used as hydrofoils in the design of underwater de- 
vices have been determined in wind tunnels and in 
general include only the hydrodynamic forces and 
moments as functions of angle of attack and of Rey- 
nolds number. Aside from approximating the pres- 
sures and velocities at which cavitation mil first 
appear (with the aid of measured pressure distribu- 
tions along the surface of the shape), no information 
is obtained about the beginning and growth of cavi- 
tation nor about the forces acting on the hydrofoil 
during cavitation. Such data can be obtained only in 
a water tunnel. This chapter includes a typical set of 
water tunnel measurements of hydrofoil character- 
istics including forces and moments Avithout cavita- 
tion and photographic observations of the develop- 
ment of cavitation. The results are also compared 
with the available wind tunnel data on the same 

shape. 

^ ^ Installation and Tests 

The profile tested is identical to the 4412 airfoil 
section of the National Advisory Committee for 
Aeronautics, and is called the NACA 4412 hydrofoil 
here. Its dimensions are shown in Figure 1 where the 
profile is sketched in the zero angle-of-attack posi- 
tion. For the experiments, solid stainless steel test 
sections^ with a chord of 3 in. were supported at one 
tip by the water tunnel balance spindle and canti- 
levered into the working section. By rotating the 
spindle, the hydrofoil angle of attack could be 
changed. A special arrangement of the working sec- 
tion was used where a 3.33 aspect ratio hydrofoil test 
unit spanned a 10-in. gap between parallel tunnel 
walls. This installation, Avhich gave approximately 
two-dimensional flow, is shown in Figures 2 and 3. 
Two different hydrofoil installations were used, per- 
mitting measurements of the hydrodynamic forces 


® These test sections were supplied by the David Taylor 
Model Basin. 


and moments acting on the complete 10-in. span or on 
only one-half the span. The latter was obtained by 
splitting the hydrofoil at the tunnel centerline and 
supporting one-half independently of the tunnel 
balance. For measurements at angles of attack both 
halves were rotated through the same angle. 

Two types of experiments were made. The first was 
the determination of the hydrodynamic lift, drag, 
and pitching moment as functions of the angle of 
attack for cavitation-free operation at Reynolds 


Station 

Upper 

Lower 

Slot ion 

Upper 

Lower 

0 

_ 

0 

40 

9.80 

-L80 

1.25 

2.44 

-\AZ 

50 

9J9 

-1.40 

2.5 

3.39 

-1.95 

60 

8J4 

-1.00 

5J0 

4.73 

-2.49 

70 

6.69 

-0.65 

7.5 

5.76 

-2.74 

80 

459 

-0.39 

10 

659 

-2.86 

90 

2.71 

-0.22 

15 

7.89 

-2JB8 

95 

1.47 

-ai6 

20 

8.80 

-274 

100 

ai3 

-ai3 

25 

9.41 

-250 

100 

— 

0 

30 

9.76 

-2.26 








30 40 50 60 70 

PER CENT OF CHORD 


90 100 


LEADING EDGE RADIUS 00158 x CHORD 
SLOPE OF RADIUS THROUGH END OF CHORD 4/20 
MAXIMUM MEAN CAMBER » a04 x CHORD 

LOCATION OF MAXIMUM CAMBER - a4 x CHORD 
MAXIMUM THICKNESS - 0.12 x CHORD 

Figure 1. Dimensions of the NACA 4412 airfoil. 


numbers of from 287,000 to 903,000. The second was 
the observation of the inception and growth of cavi- 
tation at different angles of attack as functions of 
velocity and pressure. The effect of cavitation on the 
lift and drag was investigated qualitatively but de- 
tailed investigations were postponed because of the 
limited time available for the tests. 


18.1.3 Infinite Aspect Ratio Characteristics 
of the NACA 4412 Hydrofoil 

Because of the two-dimensional character of the 
water tunnel test installation, the measured hydrody- 
namic forces and moments approximate Avithout 


259 


260 


TWO-DIMENSIONAL BODIES 



Figure 2. Hydrofoil test installation. 


These effects, which arise because of the large 
‘‘leakage” of fluid at the tips of the foil from the high- 
pressure bottom surface to low-pressure top surface, 
reduce the lift and increase the drag at given angles 
of attack. The magnitude of the effects is different 
for changing aspect ratios, plan form, and twist of 
the section. Because of the absence of these secondary 
influences, infinite aspect ratio results are also called 
“section characteristics,” denoting that they repre- 
sent the basic behavior of the profile shape of the foil 
independent of aspect ratio or other geometrical 
configurations. Data in this form are particularly 
useful to the designer of wings, propeller blades, or 
other lifting or pumping devices. Several methods 
have been developed for converting section charac- 
teristic data into the performance of finite span units 
with either uniform or varying sections.^*"’*®’®^ 

Terms and Symbols 

The terms and symbols most widely used for de- 
scribing infinite aspect ratio characteristics are those 
developed for the aeronautics field. These differ in 
some respects from those normally used for reporting 
water tunnel data and, consequently, must be defined 
here. The following list includes all the definitions 
used in this chapter: 


further correction the characteristics of a hydrofoil 
section with infinite aspect ratio. Infinite aspect 
ratio characteristics differ from those obtained by 



Figure 3. View looking downstream into tunnel work- 
ing section with the parallel walls and hydrofoil test 
span in place. 

tests of a finite span airfoil or hydrofoil because of 
the occurrence for the finite span of the so-called 
“induced” effects.'^*"’'^^ 


ri jiM'inKvrm. J 



CHARACTERISTICS OF HYDROFOILS-THE NACA 4412 SECTION 


261 


ao = angle of attack between hydrofoil and 
the mean flow direction of the water, in 
degrees. 

do = drag force per unit length of hydrofoil 
span, in pounds. 

lo = lift force per unit length of hydrofoil 
span, in pounds. 

mac = pitching moment per unit length of hy- 
drofoil span, in foot-pounds, measured 
about the aerodynamic center. 

V = relative velocity between the water and 
the hydrofoil, in feet per second 
p = density of water, in slugs per cubic foot. 
fx = absolute viscosity of water, in pounds- 
seconds per square foot. 
c = chord of hydrofoil section, in feet. 
h = span of hydrofoil test unit, in feet. 
bjc = aspect ratio. 

ac = aerodynamic center, the point about 
which the pitching moment coefficient 
is independent of lift. 

CP = center of pressure, the point at which 
the resultant of all the hydrodynamic 
forces acting on the hydrofoil is applied. 

Section Profile Drag Coefficient 

_ do 
Pyc 

Section Lift Coefficient 



Section Pitching Moment Coefficient (about aero- 
dynamic center) 

^"»ac 

Pyc^ 

Reynolds Number 

R = ^- 

Cavitation Parameter 



where in addition to terms defined above 

= absolute pressure in the undisturbed 
flow, in pounds per square foot, 

Pb = pressure in the cavitation bubble (taken 
as equal to the vapor pressure of water 
for these tests) , in pounds per square foot. 


18.1.5 Measured Characteristics 

The hydrodynamic characteristics without cavita- 
tion are shown in Figure 4, which is a diagram of 
angle of attack, drag, and pitching moment coeffi- 
cients as functions of the lift coefficient. These data 
are derived directly from the water tunnel measure- 
ments without corrections of any kind. They include 
the Reynolds number range from 287,000 to 903,000 
and were obtained with the semispan installation. 
Tests with the full span which were limited to Rey- 
nolds numbers below 388,000 gave the same results 
and were not included in the diagram. The magni- 
tudes for the important characteristics for both 
semi- and full-span installations are given in Table 1. 

The curves show certain consistent changes in per- 
formance with Reynolds number. With increasing 
Reynolds number the maximum lift coefficient in- 
creases while the angle of attack for zero lift and the 
profile drag both decrease. The pitching moment 
about the aerodynamic center remains essentially 
independent of Reynolds number up to a lift coeffi- 
cient of about 0.8 (angle of attack of +4 degrees). 
Moreover, its magnitude is essentially constant in 
this range. 


18 . 1.6 Deviations from True Infinite 
Aspect Ratio Characteristics 

The only deviations of these results from real two- 
dimensional characteristics will be caused first, by 
variation of velocity along the span of the hydrofoil 
from the center of the working section on through 
the boundary layer to the tunnel wall; second, by 
flow through the clearance spaces between the ends 
of the foil and the tunnel walls or between the two 
halves of the split-span installation; and third, by 
interference from the tunnel walls. 

Deviations from a uniform velocity distribution 
will tend to make all the coefficients numerically 
high. However, as shown in Figure 2, the hydrofoil 
test unit was located in the measuring section about 
one “diameter” downstream from the final contrac- 
tion of the flow. With so short a distance the bound- 
ary layer growth should be small. Consequently, 
along most of the hydrofoil span the flow should have 
the full velocity of the central uniform portion of the 
velocity profile, and the resulting hydrodynamic 
forces and moments should be reasonably accurate 
for infinite span. 


ANGLE OF ATTACK, OT., DEGREES 


262 


TWO-DIMENSIONAL BODIES 



/ 


Figure 4. Infinite aspect ratio characteristics of the NACA 4412 hydrofoil section. 


SECTION PITCHING MOMENT COEFFICIENT, C„ SECTION PROFILE DRAG COEFFICIENT, 


CHARACTERISTICS OF HYDROFOILS -THE NACA 4412 SECTION 


263 


Table 1. Principal section characteristics of the NACA 4412 hydrofoil from two-dimensional tests in water tunnel. 


Attack Aerodynamic center 



Test 

Reynolds 

number 

angle for 
no lift 

ai^ in degrees 

Lift curve 
slope 

ao per degree 

Max lift 
coefficient 

Cjmax 

Min drag 
coefficient 

CdO min 

Pitching 

moment 

Cm AO 

Ahead 
of c/4 in 
per cent of c 

Above 
chord in 
per cent of c 

Semispan 

287,000 

-3.95 

0.098 

1.36 

0.014 

- 0.102 

5.47 

- 0.26 

installation 

563,000 

-4.05 

0.102 

1.39 

0.013 

- 0.101 

4.92 

- 4.52 


730,000 

-4.15 

0.104 


0.0105 

- 0.102 

5.53 

- 3.84 


903,000 

-4.25 

0.106 


0.011 

- 0.101 

5.39 

1.68 

Full-span 

299,000 

— 4 (approx)* 

0.098 

1.38 

0.014 

-0.100 

5.12 

- 0.38 

installation 388,000 

Theoretical values for 

— 4 (approx)* 

0.101 


0.014 

- 0.102 

5.12 

- 0.39 

infinite aspect ratio 

-4.58 

0.120 



- 0.137 

0 

0 


♦These values for ai^ are obtained after correction for error in initial alignment of hydrofoil chord with tunnel axis. 


The principal effect of leakage flow through the 
gaps between the tunnel walls and the hydrofoil and 
between the ends of the split hydrofoil will be to re- 
duce the actual angle of attack at the hydrofoil for 
high lifts. All clearance gaps were held to approxi- 
mately 0.005 in., so that the resistance to flow through 
them was high. At small angles of attack the influence 
on the measured forces and moments should be neg- 
ligible. However, as the lift increases, enough leakage 
flow may occur to reduce the maximum lift coefficient 
appreciably. This is an error in lift and moment that 
would be reduced by using end plates set into the 
tunnel walls instead of clearance gaps. However, such 
a setup would not be as satisfactory an arrangement 
for measuring drag. It should be emphasized that the 
clearance gap effect is important so that good control 
of the gap is essential. Measurements made with the 
clearance varied indicated that for a moderate range 
of the lift coefficient the errors in measurements 
made with 0.005-in. gap were probably not more 
than 2 per cent. 

Tunnel wall interference changes the streamline 
pattern around the hydrofoil from that in a free 
stream. The walls parallel to the pitching axis are im- 
portant for two-dimensional flow and it was with 
this in mind that the maximum dimension normal to 
the hydrofoil axis was held to the full 14 in., as shown 
in Figure 1. Wall interference, including the so-called 
“blocking” or actual restriction of the passage by 
the test unit itself, is negligible at low lift (small 
angles of attack). At high lifts it is much more im- 
portant and should show greatest effect at the maxi- 
mum lift. The actual magnitude of the wall inter- 
ference has not been evaluated. 

To summarize, it appears that these tests give 
accurate results in the low-lift range, the normal 
range of application for hydrofoils. At high lifts, the 


accuracy is lower but good comparative results are 
still obtainable. 

18.1.7 Theoretical Characteristics 

It is of interest to compare these water tunnel 
measurements with the characteristics that can be 
calculated from theoretical consideration of an infi- 
nite-span section in a non viscous fluid.^*" Such a treat- 
ment gives, for small angles of attack, a lift coefficient 
proportional to the angle of attack, an attack angle 
for zero lift proportional to the amount of camber, 
and a moment coefficient constant about the quarter- 
chord point. Since frictionless flow is assumed, the 
theoretical values are independent of Reynolds num- 
ber. Also, because of the zero friction assumption, 
this treatment gives zero drag and gives no informa- 
tion about the maximum lift coefficient to be ob- 
tained. Comparison in Table 1 of the theoretical 
values with the measured values shows that the 
former are slightly higher (numerically) in each case. 

^ * Comparison with Wind Tunnel 
Measurements 

The 4412 profile has been thoroughly tested in the 
NACA variable-density wind tunnel and its charac- 
teristics reported in a series of technical reports.^'^ 
These measurements were made on finite rectangular 
span sections having an aspect ratio of 6 and the data 
were then corrected to get the infinite aspect ratio or 
section characteristics. In Figure 5, two of the water 
tunnel tests are compared with two of the wind tun- 
nel tests for comparable Reynolds numbers. The 
wind tunnel data are not corrected for turbulence or 
scale effects and should not be confused with final 
characteristics, presented in the later NACA re- 




ANGLE OF ATTACK, OC. , DEGREES 


264 


TWO-DIMENSIONAL BODIES 



Figure 5. Comparison of NACA 4412 hydrofoil characteristics from wind tunnel and water tunnel tests. 



CHARACTERISTICS OF HYDROFOILS-THE NACA 4412 SECTION 


265 


Table 2. Principal section characteristics of the NACA hydrofoil from wind tunnel tests of rectangular airfoils with aspect 
ratio = 6*. 


Attack Aerodynamic center 


Test 

angle for 

Lift curve 

Max lift 

Min drag 

Pitching 

Ahead 

Above 

Reynolds 

no lift 

slope 

coefficient 

coefficient 

moment 

of c/4 in 

chord in 

number 

in degrees 

ao per degree 

Cimax 

CdO min 

Cmac 

per cent of c 

per cent of c 

331,000 

-4.35 

0.094 

1.27 

0.011 

- 0.096 

1.1 

-8.0 

638,000 

-4.25 

0.094 

.1.36 

0.012 

- 0.094 

1.0 

- 1.0 


♦Wind tunnel data were taken from Figure 7 of the NACA Technical Report 669, and corrected by the methods outlined on pages 17 and 18 of that 
reference to give so-called “second approximation” characteristics. 


ports/^^* which have been extrapolated to full-scale 
aircraft flight Reynolds numbers. In Table 2, the 
principal characteristics from the wind tunnel tests 
for these two Reynolds numbers are listed for com- 
parison with the water tunnel values given in Table 
1. Both the figures and tabulations show some dif- 
ferences between the two sets of measurements. The 
angles for zero lift are comparable, while the mini- 
mum drag coefficient, the rate of change of lift with 
angle of attack, and the moment coefficient are all 
about 10 per cent lower in the case of wind tunnel 
measurements. The latter two represent more marked 
deviation from the theoretical values than shown by 
the water tunnel characteristics. The wind and water 
tunnel minimum drag coefficients are comparable at 
the higher Reynolds number but differ considerably at 
the lower R values. The maximum lift coefficient is 
higher for the water tunnel tests. 

It is seen that the water tunnel results are as good 
or better than the corresponding wind tunnel data. 
Furthermore, they are obtained directly from tunnel 
measurements without corrections of any kind, 
whereas the finite span tests must be treated elabo- 
rately to obtain approximate infinite aspect ratio 
characteristics. Even at large attack angles where the 
water tunnel data may be in error, the results are as 
satisfactory as those from the other type of tests. 

18.1.9 Reynolds Number and Turbulence 
Effects for Tests and Applications 

The range of Reynolds numbers covered by the 
water tunnel tests includes the values characteristic 
of many hydrofoil applications. For very large pro- 
pellers, R will exceed 1,000,000, but for many pump, 
turbine, and small propeller applications, R is less 
than that figure. For application outside the range of 
the tests the data must be extrapolated and cor- 
rected. For test Reynolds numbers up to about 
3,000,000, wind tunnel measurements have indicated 


that the lift curve slope increases only 1 or 2 per cent 
beyond its value at = 1,000,000. The angle for zero 
lift and the pitching moment coefficient are also 
affected only slightly. However, the maximum lift 
coefficient increases 10 per cent to 20 per cent and the 
profile drag coefficient decreases at approximately 
the same rate as the turbulent skin-friction drag on 
flat plates. By judicious application of such rules the 
useful range of these results can be extended appreci- 
ably. 

Actually, the performance measured in the tunnel 
will differ from free-stream behavior because of dif- 
ferences in turbulence. High turbulence in the tunnel 
working section will cause high maximum lift co- 
efficients and will influence the boundary layer transi- 
tion on the hydrofoil and hence coq. There are meth- 
ods proposed for compensating for tunnel turbulence 
by assuming the results apply at higher than test 
Reynolds numbers, but these procedures are of ques- 
tionable accuracy for all but corrections and 
were not applied to the water tunnel data. 

18.1.10 Cavitation Characteristics 

The continuity of the behavior of airfoils when 
used in the normal range of velocities below the sonic 
is limited by “separation” of the flow for large angles 
of attack. For the same shape used as a hydrofoil in a 
liquid instead of a gas, the continuity in behavior can 
be interrupted by cavitation as well as by separation. 
Cavitation first occurs when, because of flow accele- 
rations caused by the curvatures of the hydrofoil, the 
local pressure at any point on or near the hydrofoil is 
reduced to the vapor pressure of the liquid. This re- 
sults in local boiling and vapor bubble formation. 
These bubbles collapse as they are swept into higher 
pressure zones. As the flow velocity is increased or as 
the general pressure level is reduced, the extent of the 
low-pressure zone is enlarged and the volume occu- 
pied by cavitation bubbles increases. 


Cl ^M'IDI NTUI. 7 


266 


TWO-DIMENSIONAL BODIES 


The interest in cavitation lies in the fact first, that 
when it begins, the lift on the hydrofoil (or thrust for 
propellers) drops off sharply and the drag simultane- 
ously increases; second, prolonged cavitation causes 
physical damage to the hydrofoil blade itself. Cavita- 
tion erosion of propellers and turbine impellers are 
two outstanding examples of this latter. 


appearing on the diagram refer to figures in the re- 
port and the coordinates of the points marked by the 
numbers indicate the attack angle and K value at 
which each picture was taken. Thus the relationship 
between conditions for inception of cavitation and 
the conditions for each figure is shown graphically. 


Cavitation Photographs 

Figures 7 to 13 inclusive make up a photographic 
study of the inception and growth of cavitation on 
the NACA 4412 hydrofoil. These flash photographs 



Figure 6. Diagram showing cavitation test conditions 
for each photograph in Figures 7 to 13. 


of about 20 Msec exposure were obtained at constant 
water speed and variable pressure. They include the 
development of cavitation on one or both faces of the 
hydrofoil for attack angles ranging from 4 to 12 de- 
grees. The photographs are grouped according to 
angle of attack, each group arranged to show the 
development of cavitation as the pressure and hence 
the cavitation parameter K is reduced. Figure 6 is a 
diagram that will be useful in discussing the signifi- 
cance of the pictures. It is a graph of the cavitation 
parameter K plotted against the angle of attack ao- 
A curve marks the inception of cavitation on the 
upper and the lower surface of the hydrofoil. In the 
area above this curve there is no cavitation, while 
everywhere below the curve cavitation exists in 
varying degrees, increasing with the reduction of K 
below the incipient value. The numbers of 7 A to 13D 


Angle of Attack and Cavitation Inception 

It will be noted in Figure 6 that for both large 
positive and large negative angles of attack, cavita- 



Figure 7. Cavitation on lower surface. a = —4°. V = 
45 feet per second. Flow right to left. 


tion occurs “early,” that is, at high pressures or low 
velocities and hence high K values. At angles near 
zero, cavitation is delayed, the minimum critical K 
falling at about 0.66 at Q!o = — 1.4°. Thus, Figure 12A 
shows cavitation soon after inception at A = 1.8 for 
ao = +8°, while Figure 9A shows an early stage of 
cavitation at A = 0.57forQ!o = 0°. This is caused by 
the fact that with increasing attack angle the leading 
edge of the hydrofoil, where the profile curvature is 
large, is turned at an angle to the flow and the water 


■ipCNti fr7 



CHARACTERISTICS OF HYDROFOILS -THE NACA 4412 SECTION 


267 


must curve sharply to follow it. Consequently, the 
local acceleration of the fluid is large and the vapor 
pressure is reached locally even with high static pres- 
sure in the maiu flow. Cavitation occurs first on the 
top surface of the hydrofoil for all positive angles and 
for negative angles do\\Ti to —1.4° because it is the 
low-pressure side for those attack angles. At negative 
angles beyond — 1.4°, however, the higher pressure is 
obtained at the top and cavitation occurs first on the 
lower surface. Thus in Figure 7A, for a = —4°, the 
beginning of cavitation is shown near the leading 
edge of the lower side of the hydrofoil. 

It is interesting to note that the best cavitation 
performance does not occur at the angle of attack for 



Figure 8. Cavitation on lower surface. q; = 0°. F =45 
feet per second. Flow right to left. 


zero lift. At ao = — 1 .4°, which has the minimum value 
oiK = 0.66 for incipient cavitation, the lift coefficient 
is0.26(/^ = 287,000) whereas at ao = —3.95°, which 
is the attack angle for zero lift, the K for incipient 
cavitation is 1.30. 

At high angles of attack cavitation occurs only on 
one surface of the hydrofoil. There is a sufficient dy- 
namic pressure increase on the surface pitched into 
the stream to suppress cavitation completely. Fig- 
ures 11 A to 12D show that for ao = 8°, no cavitation 
is obtained on the lower surface of the hydrofoil even 
though K is reduced to 0.26, while on the upper sur- 
face cavitation is well established at A = 1.8. For 
angles near zero, cavitation occurs first on the upper 
or low-pressure surface and then also occurs on the 
high-pressure surface as K is reduced. For example, 
at a = 0°, the lowest pressure occurs on the top of the 
hydrofoil and Figure 9B shows well developed cavi- 


tation there with K = 0.42. By contrast. Figure 8 A 
shows the bottom surface SitK = 0.37 with cavitation 
in an early stage. There the beginning of cavitation 
on the lower side is seen with trailing wisps of the 
more fully developed cavitation from the top 
appearing at the left. 


Cavitation Bubble Growth 

A certain similarity exists for each sequence of 
photographs for one angle of attack. Cavitation be- 



Figure 9. Cavitation on upper surface. a=0°. F =45 
feet per second. Flow left to right. 


gins on the forward part of the hydrofoil as a narrow 
zone of small bubbles. The bubbles are individually 
distinguishable in some cases but coalesce to form 
“sudsy” zones in others. The limit of the zone of 
bubbles is a rough measure of the extent of the low- 
pressure area on the hydrofoil surface. As the pressure 
is reduced the low-pressure area is broadened and the 
vapor bubbles are swept farther back before collaps- 
ing, until they form a sheet hiding the hydrofoil and 
extending downstream more than 6 or 8 chord 
lengths, completely past the limits of the working- 
section windows. (See Figures 9D, lOD, etc.) For any 
given pressure and velocity the cavitation bubble 
grows until the rate of vapor entrainment by the 
water balances the rate of vapor formation within the 
bubble. Thus the magnitude of the cavitation zone in 


268 


TWO-DIMENSIONAL BODIES 


each of the photographs represents a “steady-state” 
condition for the given value of K. 

As Figures 7A to 8C show, the fine-grain sudsy 
type of bubbles are obtained where the minimum 
pressure is caused by a sharp curvature such as occurs 
at the leading edge of the lower hydrofoil surface. 
Figures 9A to D, on the other hand, show the forma- 
tion of transparent, relatively large individual bub- 
bles on the upper surface. Here the minimum pressure 
is obtained where the profile has a more gentle curva- 
ture. As the hydrofoil is given large angles of attack 



= 0.62 


* 0,30 


0.2 4 
BACK 
LIGHTtNC) 


* 0,2 4 


Figure 10. Cavitation on upper surface. a= +4°. 
F=45 feet per second. Flow left to right. 


(Figures 13A to D at a = +12°), the minimum-pres- 
sure point moves forward to a place where the curva- 
ture of the upper surface is sharper and the sudsy 
bubbles are again obtained. 

Under some conditions the forward portion of the 
large enveloping bubble for fully developed cavita- 
tion is transparent. That is, the interface between the 
cavitating zone and the surrounding water is a 
smooth surface, free of disturbances. An example of 
this is shown in Figure 7E where the hydrofoil itself 
and the disturbance from cavitation on the opposite 
face of the hydrofoil are clearly visible through the 
bubble enveloping the near surface. The smooth in- 
terface is an indication that very little vaporization 
is occurring through that surface. Most of the vapor 
that is being supplied to the bubble comes from the 


turbulent boiling zone near the downstream end of 
the envelope. Figure 9D shows how the bubbles tend 
to coalesce as the pressure is reduced to form the 
single large transparent envelope. The transparency 



Figure 11. Cavitation on lower surface. a= -|-8°. V = 
45 feet per second. Flow right to left. 



Figure 12. Cavitation on upper surface, a. = +8°. V = 

45 feet per second. Flow left to right. 

cannot always be reproduced, but rather seems to 
occur randomly unless some external disturbance, 
such as a piece of trash hanging to the foil or a nick in 
its surface, is introduced to accelerate the formation. 
Figure 8B shows the effect of small disturbances at 
the leading edge in forming long, extended bubbles. 
Such disturbances also cause cavitation to occur at 
higher pressures (or lower velocities). 

Note that the individual bubbles grow from the 
time of their formation until they collapse. In Figure 


CHARACTERISTICS OF HYDROFOILS-THE NACA 4412 SECTION 


269 


IOC measurements of the average bubble size showed 
that growth was rapid for the first quarter chord 
length of travel, attaining 60 to 75 per cent of what 
appears to be the final diameter. Beyond this the 



Figure 13. Cavitation on upper surface. a= +12°. 
F =32 feet per second. Flow left to right. 


bubbles grow more slowly until they interfere with 
their neighbors and finally are entrained and collapse. 
The interior of the cavitation bubble is at the vapor 
pressure of the water and is maintained at this pres- 
sure by the “pumping” action of the water. The 


VELCX5ITY, FT PER SEC 

0 10 20 30 40 50 60 70 80 90 100 110 120 



growth of the bubbles is probably evidence of con- 
tinual vaporization into each bubble cavity until the 
bubble itself is swept into a higher pressure zone. 

Critical K Compared with Predictions from 
Wind Tunnel Data 

Figure 14 is another diagram showing values of 
the cavitation parameter K for incipient cavitation 



Figure 14. Values of K at which cavitation begins 
versus angle of attack. 


versus the angle of attack a^. This diagram covers a 
much wider range of angles than Figure 6 and in- 
cludes, in addition, a curve predicted from wind tun- 
nel measurements of the pressure distributions on the 
4412 profile.'^® The agreement between ^the water 
tunnel curve and the predicted curve is good only for 
small positive angles of attack, while for increasing 

ANGLE 01^ ATTACK, «^o , DEGREES 



Figure 15. Submergence required to prevent cavitation on NACA 4412 hydrofoil. 






270 


TWO-DIMENSIONAL BODIES 


ao, either negatively or positively, the water tunnel 
tests indicate a “delay” in reaching the inception 
point. A similar deviation from pressure-distribution 
predicted values for inception has been observed in 
case of some projectile shapes. As discussed in 
Chapter 6, the reason for the deviation is not known 
definitely, but may be associated with the ability of 
the fluid to stand a slight tension. 

Submergence Required to Prevent Cavitation 

Figure 15 shows the submergence required to pre- 
vent cavitation on the 4412 hydrofoil as a function of 
velocity and angle of attack. The term “submergence” 
means the vertical depth below the water surface 
(e.g., ocean surface). The curves are calculated for 


fresh water at 60 F and 14.7 psi atmospheric pressure. 
In each of the two diagrams the vertical distance 
down from the horizontal axis represents the sub- 
mergence required to prevent cavitation at a given 
attack angle or given velocity. All points below the 
constant ao or constant v curves represent cavitation- 
free operation. 

It is clear from the left diagram that for any 
velocity, the minimum submergence will be required 
for cavitation-free operation if ao = —1.4°. For all 
other angles of attack, the necessary submergence is 
greater. In the right diagram the limiting range of 
angles at given velocities and submergences are 
emphasized. For example, at 60 fps and 15 ft sub- 
mergence, cavitation-free operation is possible only 
within the limits of —2.4° and +2.6°. 


Chapter 19 


MISCELLANEOUS INVESTIGATIONS 


19 1 FLUID FRICTION LOSSES 

IN 0.50-CALIBER GUN BARRELS 

19.1.1 Purpose of Investigation 

T wo ASSOCIATED problems in the internal ballistics 
of guns arise from the rapid expansion of the 
powder gases. One is the reduction in effective force 
applied at the projectile as a result of the pressure 
drop caused by fluid friction, and the other is the 
influence of the friction effects on heat transfer. The 
measurements described here were made to deter- 
mine the effect of rifling on the friction pressure drop 
and to determine by analogy with the fluid friction 
laws the effect on turbulence and, hence, on heat 
transfer. 


I = length in feet of the barrel or tube be- 
tween pressure taps, 

V = mean velocity in feet per second, 
g = acceleration of gravity in feet per second 
per second, 

d = diameter of the tube in feet or 

= (IA/tt)^ for the rifled barrel, when A is 
the actual cross-sectional area. 

The Reynolds number is calculated from the equation 

^ _ vdp _ ^ 

p V 

where v — pjp — kinematic viscosity in square feet 
per second. 


Material Tested 


Test measurements were recorded for two barrels. 
These barrels were standard except that one had no 
rifling. Their comparative dimensions and conditions 
are indicated as follows: 


Rifled Barrel Unrifled Barrel 


Bore diameter 
Maximum diameter 
Rifling groove depth 
Rifling groove width 
Land width 
Area of cross section 
normal to barrel axis 
Equivalent diameter 
Twist of rifling 
Surface condition 


Barrel length 
Distance between 
pressure taps 


0.500 in. 
0.507 in. 
0.0035 in, 
0.125 in. 
0.071 in. 


0.500 in, 
0.500 in. 
None 
None 
None 


0.1999 sq in. 
0.5045 in. 

1 turn in 30.5 calibers 
Spiraled boring tool 
marks on lands were 
not so deep as for un- 
rifled barrel. Broach- 
ing tool marks along 
length of each groove 
3.349 ft 


0.1964 sq in. 
0.500 in. 

None 

Close spaced, 
spiraled boring 
tool marks 
throughout 
barrel length 

3.349 ft 


3.646 ft 3.646 ft 


Friction Factor 


The friction factor was evaluated for both barrels 
from the equation 

///=/ \v^l2dg ( 1 ) 

where Hf = friction loss in feet of the fluid flowing, 
/ = friction factor, 


^ ^ Results Obtained 

Figures 1, 2, and 3 are graphical representations of 
the results obtained. 

Figure 1 shows that, for the same rate of flow, the 
unrifled barrel offers approximately 4 per cent more 
resistance than hydraulically smooth tubing"^ of 
0.500-in. diameter, while the rifled barrel offers 
about 3 per cent less. Several factors contribute to 
this difference. The effective area of the rifled barrel 
normal to the centerline is greater than for an 0.500- 
in. diameter tube and this lowers the velocity and 
resistance. In addition, the unrifled barrel is hydrau- 
lically rougher and shows boring tool marks which 
appear to be deeper than any of the boring or longi- 
tudinal broaching marks on the rifled piece. Appar- 
ently, because of this very gradual twist, the rifling 
grooves do not constitute roughness in the normal 
sense. Note that they did not cause enough rotation 
of the water to affect the pressure at the downstream 
measuring point. The friction factors for both barrels 
approach that of a smooth tube so closely that, for 
practical purposes, they can be assumed to be smooth 
tubes. 

Figure 2 presents the relation of the friction loss to 
the Reynolds number. 

Figure 3 presents the relation of the friction factor 
to the Reynolds number. The curve for the unrifled 

^ The resistance for hydraulically smooth tubing is calcu- 
lated^^ from the Kdrmdn-Nikuradse equation (l/\/7) = 

- 0.8 -b 2.0 log , 0 (/2V7). 


271 


FRICTION LOSS, FT OF FLUID PER FT OF TUBE 


272 


MISCELLANEOUS INVESTIGATIONS 



REYNOLDS NUMBER, R = 

Figure 1. Friction factor versus Reynolds number for 0.50-caliber rifled and unrifled gun barrels. 




Figure 2. Friction loss per unit length of tube versus 
Reynolds number. For 0.50-caliber rifled and unrifled 
gun barrels. 


Figure 3. Friction loss per unit length of tube versus 
discharge in cubic feet per second for 0.50-caliber rifled 
and unrifled gun barrels. 




FLUID FRICTION LOSSES IN 0.50-CALIBER GUN BARRELS 


273 


barrel has the same position relative to that for 
smooth tubes as in the previous figures. However, 
the curve for the rifled barrel also falls above the 
smooth-tube curve. This is to be expected when it is 
considered that Figure 3 is for the friction factor 
calculated for the actual cross section which is larger 
in this case. 

The results of many investigations of friction loss 
of different types of tubes have shown that the fric- 
tion pressure drop at Reynolds numbers between 
100,000 and 1,000,000 depends on the type of surface 
roughness.®®’^^^ If the roughness is produced by ir- 
regular projections randomly spaced, / becomes con- 
stant as Reynolds number is increased. However, if 
the roughness is produced by waviness in the pipe 
wall, the curve oi f vs R continues approximately 
parallel but above that of the hydraulically smooth 
tube. At extremely high Reynolds numbers, most ex- 
periments show that rough tubes and pipes assume a 
constant value of /. Because of these differences, the 
relation observed in Figure 3 between the curves for 
smooth tubes and for the gun barrels may not hold 
exactly if R is further increased. It is possible that the 
actual friction drop curve for the gun barrels may 
pass through a transition to give a constant / of 


approximately the measured value or possibly slightly 
higher or, as R increases, it may continue parallel to 
the smooth-pipe curve. In Figure 3 are shown values 
for new steel pipes which might be considered to have 
a wavy-type surface. A curve is also shown for arti- 
ficially roughened pipe having an irregular type of 
roughness produced by sand grains whose diameters 
averaged 1/507 times the tube radius. These two 
curves are shown as an indication of the trends 
which could be expected and not as a measure of 
extrapolated values. Actually, the deviation of the 
curves for the gun barrels is so slight and the charac- 
ter of the surface is so different from sand-grain 
roughness, it may be expected that / will continue 
parallel to the smooth-tube curve in a manner similar 
to that of the steel pipe curve shown. 

The similarity between the fluid friction factor 
curves in Figure 3 for the rifled and unrifled barrels 
indicates a similar degree of development of the 
boundary layer and of friction turbulence. It is not 
expected, therefore, that the law of heat transfer 
should be materially different with rifling than with- 
out. Assuming the continued agreement of friction 
factors at higher Reynolds numbers, this conclusion 
should also hold under actual firing conditions. 


CONFIUF^TIAL 


rp • 



APPENDIX 


DEFINITIONS OF SPECIAL TERMS 
• AND FORMULAS 

The purpose of this Appendix is to present the 
definitions of special terms and the formulas used 
frequently throughout this volume in a compact and 
convenient form for ready reference. Any additional 
definitions may be found in the Glossary. 

DEFINITIONS 

Yaw Angle, xj / 

The angle, in a horizontal plane, which the axis of 
the projectile makes with the direction of motion. 
Looking down on the projectile, yaw angles in a 
clockwise direction are positive (+) and in a counter- 
clockwise direction, negative ( — ). 

Pitch Angle, a 

The angle, in a vertical plane, which the axis of the 
projectile makes with the direction of motion. Pitch 
angles are positive (-|-) when the nose is up and 
negative ( — ) when the nose is down. 

Lift, L 

The force, in pounds, exerted on the projectile 
normal to the direction of motion and in a vertical 
plane. The lift is positive (T) when acting upward 
and negative ( — ) when acting downward. 

Cross Force, C 

The force, in pounds, exerted on the projectile 
normal to the direction of motion and in a horizontal 
plane. The cross force is positive when acting in the 
same direction as the displacement of the projectile 
nose for a positive yaw angle, i.e., to an observer 
facing in the direction of travel, a positive cross force 
acts to the right. 

Drag, D 

The force, in pounds, exerted on the projectile 
parallel with the direction of motion. The drag is 
positive when acting in a direction opposite to the 
direction of motion. 

Moment, M 

The torque, in foot-pounds, tending to rotate the 
projectile about a transverse axis. Yawing moments 


tending to rotate the projectile in a clockwise direc- 
tion (when looking down on the projectile) are posi- 
tive (+), and those tending to cause counterclock- 
wise rotation are negative ( — ). Pitching moments 
tending to rotate the projectile in a clockwise direc- 
tion (when looking at the projectile from the port 
side) are positive (-f), and those tending to cause 
counterclockwise rotation are negative ( — ) . 

In accordance with this sign convention a moment 
has a destabilizing effect when it has the same sign 
as the yaw or pitch angle. 

In all model tests the moment is measured about 
the point of support. Moments about the center of 
gravity of the projectile have the symbol, Meg. 

Normal Component, N 

The sum of the components of the drag and cross 
force acting normal to the axis of the projectile. The 
value of the normal component is given by the 
following : 

N = D sin \f/ C cos xjy (1) 

in which N = normal component in pounds, 

D = drag in pounds, 

C = cross force in pounds, 

\{/ = yaw angle in degrees. 

Center of Pressure, CP 

The point of intersection of the axis of the projec- 
tile and the resultant of all forces acting on the 
projectile. 

Center-of-Pressure Eccentricity, e 

The distance between the center of pressure (CP) 
and the center of gravity (CG) expressed as a decimal 
fraction of the length (1) of the projectile. The 
center-of-pressure eccentricity is derived as follows: 

e = (Lp - = j^ (2) 

in which e = center-of-pressure eccentricity, 

I = length of projectile in feet, 
leg = distance from nose of projectile to 
CG in feet, 

lep = distance from nose of projectile to CP 
in feet. 

Coefficients 

The three force and moment coefficients used are 
defined as follows. 


275 


276 


APPENDIX 


Drag coefficient : 


Cn = 


D 

y2 ’ 
P-^Ad 


Cross force coefficient: 


Cc = 


C 

y2 > 


Lift coefficient : 


Cl 


L 

y2 ’ 


This is defined as follows: 


(3) 


(4) 


in which R 

I 

V 


(5) 


P 

M 


Reynolds number, 
overall length of projectile in feet, 
velocity of projectile in feet per sec- 
ond, 

kinematic viscosity of the fluid in 
square feet per second = m/p, 
mass density of the fluid in slugs per 
cubic foot, 

absolute viscosity in pound-seconds 
per square foot. 


Moment coefficient : 


Cm = 


M 

y2 f 

P^^dI 


( 6 ) 


in which D 
C 
L 

P 

w 

g 

Ad 


V 


M 


I 


= measured drag force in pounds, 

= measured cross force in pounds, 

= measured lift force in pounds, 

= density of the fluid in slugs per cubic 
foot = w/g, 

= specific weight of the fluid in pounds 
per cubic foot, 

= acceleration of the gravity in feet per 
second per second, 

= area in square feet at the maximum 
cross section of the projectile taken 
normal to the geometric axis of the 
projectile, 

= mean relative velocity between the 
water and the projectile in feet per 
second, 

= moment, in foot-pounds, measured 
about any particular point on the 
geometric axis of the projectile, 

= overall length of the projectile in 
feet. 


Rudder Effect 

The total increase or decrease in moment coeffi- 
cient, at a given yaw or pitch angle, resulting from a 
given rudder setting. This change in moment coeffi- 
cient is measured directly from the graph of the 
moment coefficient curves for neutral rudder setting 
and various fixed rudder settings. 


Reynolds Number 


The following numerical example is for the Mark 
13-2 A torpedo operating in sea water at a tempera- 
ture of 50 F. 


F = 33 knots = 55.7 ft/sec 
V = 1.46 X 10“®sq ft/sec (for salt water) ^ 

I = 161 in. = 13.42 ft 
13.42 X 55.7 
^ ~ 1.46 X 10-5 

^ 13.42 X 55.7 X 100,000 ^ ^ x W 

(51,198,200) 


Two geometrically similar systems are also dynam- 
ically similar when they have the same value of 
Reynolds number. For the same fluid in both cases, 
a model with small linear dimensions must be used 
with correspondingly large velocities. It is also pos- 
sible to compare two cases with widely differing 
fluids provided I and V are properly chosen to give 
the same value of R. 


Cavitation Parameter 

In order to describe quantitatively the conditions 
under which cavitation occurs, the dimensionless 
cavitation parameter, K, has been defined as follows : 

K = ( 8 ) 

'’T 

in which Pl = absolute pressure in the undisturbed 
liquid, 

Pb = absolute pressure in the bubble or 
cavity, 

V = velocity of the projectile with respect 
to the undisturbed liquid, 
p = density of liquid. 


In comparing hydraulic systems where the pre- 
dominating forces are due to friction and inertia, a 


Tables of kinematic viscosity for salt water with an aver- 
age salinity of 3.5 per cent are given in Rossel and Chapman 
Principles of Naval Architecture, Society of Naval Architects 


factor called Reynolds number is of great utility^_^,^^a^ Marine Engineers, 1941, Vol. II, p. 114. 


APPENDIX 


277 


Note that any homogeneous set of units can be used 
in the computation of this parameter. It is often 
convenient to express this parameter in terms of the 
head, i.e., 


hL — hs 


( 9 ) 


where Hl = the submergence plus the baromet- 
ric head in feet of liquid, 

Hb = absolute pressure in the bubble in 
feet of liquid, 

g = acceleration of gravity in feet per 
second per second, 

V‘^/2g = the velocity head in feet of liquid. 


Any length unit can be used in equation (9) instead 
of feet. It will be seen that the numerator of both 
expressions is simply the net pressure or head acting 
to collapse the cavity or bubble. The denominator is 
the velocity pressure or head. Since the pressure 
reduction at any point on the body is proportional to 
the velocity pressure, this may be considered as a 
measure of the pressure available to open up a cavity. 
From this point of view, the cavitation parameter 
measures the ratio of the pressure available to col- 
lapse the bubble to the pressure available to open it. 
Pb is the vapor pressure of the fluid if the cavity 
contains no air or other gas. For normal cases of 
cavitation this is assumed to be true. 

If the K for incipient cavitation (Ki) is considered, 
it can be interpreted to mean the maximum reduc- 
tion in pressure on the surface of the body, from the 
pressure in the undisturbed fluid, measured in terms 
of the velocity pressure. From this it follows that, if a 
body starts to cavitate at the cavitation parameter of 
one, it means that the lowest pressure at any point on 
the body is one velocity pressure below that of the 
undisturbed fluid. It will be seen that Ki is a measure 
of the resistance of the body to cavitation, or in other 
words, an indication of the excellence of the shape. 
Thus, the lower the K for incipient cavitation, the 
greater the cavitation resistance, and the better the 
shape from this viewpoint. 

If the operating conditions (submergence and 
velocity in a given fluid medium) are such that the 
numerical value of K is greater than Ki the body will 
not cavitate. For values less than Ki more advanced 
cavitation will exist to the limit of a completely en- 
veloping cavity with an “infinite” length when K 
becomes zero. 

Using the Mark 13 torpedo as an example, 
consider how cavitation on the nose is affected by 
operation at 33 knots and 40.5 knots in sea water 
at a temperature of 50 F and a submergence of 15 
feet. 


At 33 knots 

Pl P atmos + ^sub^ 

= 14.7 X 144 T 15 X 64 = 3,080 Ib/sq ft 
Pb = 0.98 X vapor pressure of pure water at same 
temperature. 

= 0.98 X 0.178 X 144 = 25.6 Ib/sq ft 
P = 94 Ib/cu ft ^ ^ slugs/cu ft 
F = 33 knots = 55.7 ft/sec 

so that 

„ 3,080 - 25.6 3,054.4 ^ 

^ 1.00(55^7)^ = -PW = 0-99 

This is greater than Ki for the nose of this projectile, 
so cavitation will not exist. 


At 40.5 knots 


V = 40.5 knots = 68.3 ft/sec 


so that 


K 


3,080 - 25.6 


1.99 


(68.3)= 


3,054.4 

4,640 


0 . 66 . 


This is slightly below Ki for this nose so a small ring 
of cavitation will exist. 

Figure 1 gives the relation among absolute pres- 
sure, velocity, and cavitation parameter for fresh 
water at 70 F whereas Figure 2 shows the relation 
among submergence, velocity, and cavitation param- 
eter for sea water at 50 F. 


CORRECTIONS TO WATER TUNNEL 
TEST DATA 

The test data obtained from the water tunnel is in 
the form of forces and moments which indicate the 
actual hydrodynamic conditions to which the model 
is subjected in the tunnel working section. These in 
general, however, are not the conditions which would 
exist if the model were moving freely in an infinite 
body of water. Consequently, in reducing the data to 
coefficients applicable to the free-stream conditions, 
the following corrections are considered. 

Tare Drag 

The clearance between the model and the shield is 
less than 0.005 inch. With this small gap it appeared 
that the hydrodynamic force applied directly to the 


^ This approximation is obtained from Sverdrup-Johnson- 
Fleming, The Oceans, Prentice-Hall, 1942, pp. 67, 115. 

Standard properties of pure water are given in Keenan and 
Keyes, Thermodynamic Properties of Steam, Wiley, 1936. 




VELOCITY 


278 


APPENDIX 


8, 


cc 

bJ 

Q. 


KX 


& 


m 

iff- 


o. 

<0 




s- 


8 

JR- 

& 

8 

o. 

o 



Nl OS d3d S81 


»frl 

(''d-d) 


3dn6S3dd 3J.mOS0V 


o 


o 

«o 


Figure 1. Relation among absolute pressure, velocity, and cavitation parameter for fresh water at 70 F. 



VELOCITY 


APPENDIX 


279 




280 


APPENDIX 


spindle would be negligible. Consequently, no tare 
corrections are applied to the measured forces. 

Support Shield Interference 

In order to correct for the effects of interference 
with the flow around the model caused by the sup- 
porting spindle and its protecting shield, tests are 
normally made in pairs, one with and one without a 
dummy image shield on the side of the model oppo- 
site the support. The differences between the coeffi- 
cients thus obtained from each pair of tests is sub- 
tracted from the run made without image shield. 

For normal cavitation-free operation this proce- 
dure produces a result believed to be a good approxi- 
mation of free-stream conditions. With the onset and 
development of cavitation, however, the shield and 
its image produce different results depending upon 
the degree of the cavitation obtained at various val- 
ues of K. For very low i^’s the shield itself cavitates. 
As a result, the corrections determined by the above 
method vary in magnitude and, without doubt, in 
accuracy. For the full cavity stage, corrections ap- 
parently are small. In general, for the material in- 
cluded in this volume the normal corrections were 
applied for all tests which covered the incipient or the 
early stages of development. For tests which included 
only the full cavity stage, such as those described in 
Chapter 6, no corrections were applied. 

Tunnel Pressure Gradient 

The tunnel pressure gradient correction to be ap- 
plied to the measured drag for noncavitating or 
slightly cavitating conditions is evaluated by meas- 
uring the pressure gradient existing in the working 
section of the tunnel in the absence of the model. The 
pressure gradient dyjdx at each station is multiplied 
by the cross-sectional areas of the model at that sta- 
tion and the product is plotted against distance along 
model. The area under this curve gives 

0 0 

For models which are five or more diameters in length 
the calculation can be simplified by writing 


= ^ (volume), 

0 

i.e., by using the (average pressure drop) X (vol- 
ume). It is this expression that has caused the correc- 
tion to be termed ‘‘horizontal buoyancy.’’ 

Scale Effect 

Tests made in the range of 20 to 70 feet per second 
(Reynolds numbers from about 2 X lOHo 7 X 10®) 
have shown that lift, cross force, and moment coeffi- 
cients are unaffected by the scale of the tests, but 
that the drag coefficient does vary with Reynolds 
number. Extrapolation of Cd to full-scale Reynolds 
numbers depends upon the type of body and hence 
the form drag layer growth over the body. For some 
streamlined bodies, such as those with very fine 
noses, the transition between the laminar and turbu- 
lent boundary layers may shift position with change 
in Reynolds number. For these the Cd vs R curve 
may be irregular or even rising so that extrapolation 
is very difficult. In such cases it is customary to pro- 
vide some disturbance such as a small ring or a 
roughened surface at the nose of the projectile to 
assure turbulent conditions at all velocities. Extra- 
polation is based on the resulting “turbulent” 
curve. 

For bodies which do not indicate a shifting transi- 
tion region, as well as those whose boundary layers 
are made turbulent artificially, a linear extrapolation 
of Cd vs on a log-log plot has been found to give, 
in general, results that are satisfactory within the 
accuracy of the measurements. This method assumes 
that the drag coefficient (after correction for tunnel 
pressure gradient) varies inversely as the nth 
power of Reynolds number. For a projectile whose 
boundary layer is predominantly turbulent and 
whose afterbody is well streamlined, n should be 
close to Vs. Deviations from this value are the result 
of different degrees of streamlining and consequent 
effects on the boundary layer and portion of total 
drag represented by skin friction. Of course, for a pro- 
jectile whose drag is almost completely form resist- 
ance, Cd should be nearly independent of Reynolds 
number. 


GLOSSARY 


a.c. Aerodynamic center, point about which pitching moment 
is independent of lift. 

Acoustic Frequencies, See sonic frequencies. 

Ad- Area of projectile at maximum diametrical cross section 
(square feet). 

Afterbody. That portion of the projectile between the cylin- 
drical body section and the forward edge of the tail structure. 

Air Bombs. As here used, the term applies to any projectile 
which contains no propellant, is not fired from a gun, and 
whose trajectory is wholly in air. 

Angle of Attack, a. The angle between some arbitrary axis- 
of-reference in the body and its direction of motion. 

Aspect Ratio. Ratio of span to mean chord of hydrofoil 
section. 

h. Span of hydrofoil section (feet). 

b/c. Aspect ratio of hydrofoil section. 

Body. The main portion of the projectile; the projectile less 
any boom and tail surfaces. Also used frequently herein to 
refer only to the cylindrical portion of the projectile be- 
tween the nose and afterbody. 

Boom. A small diameter, cylindrical extension from the after- 
body generally used to house a rocket motor as well as to 
place the tail farther aft. 

Boundary Layer. For simplicity, it may be considered that 
the boundary layer is the relatively thin layer of fluid, any 
part of which is dragged forward by the moving projectile. 

Bourrelet. That portion of a projectile immediately aft of 
the nose, especially any part slightly larger in diameter than 
the body section following. Its function is to center the for- 
ward part and provide a bearing or guide during travel 
through the bore of the projecting device. 

Broach. To rise, break through, and spring clear of the water 
surface, 

c. Velocity of sound in medium (feet per second); chord of 
hydrofoil test section (feet). 

Cc- Cross force coefficient, 

Cd- Drag coefficient. 

Cl- Lift coefficient. 

Cm- Moment coefficient, generally referred to CG. 

CB. Center of buoyancy. 

CG. Center of gravity. 

CP. Center of pressure. 

Caliber. The maximum diameter of a projectile body. 

Cavitation Parameter, K. The ratio of the difference be- 
tween the absolute pressures in the undisturbed liquid and 
in the bubble to half the liquid density times the velocity 
squared. (Pl — PB)/hpV^’ 

Cavity. In this volume, the entrance bubble formed by the 
projectile at water entry. 


Center of Pressure, CP. The point of intersection of the 
axis of the projectile and the resultant of all forces acting on 
the projectile. 

Center of Pressure Eccentricity, e. The distance between 
the center of pressure and the center of gravity expressed as 
a decimal fraction of the length of the projectile. 

Cone Angle. As used herein, the angle formed in any plane 
section of the projectile which includes the horizontal axis, 
by the intersection of the cone sides at the vertex. 

Cross Force, C. The force exerted on the projectile normal to 
the direction of motion and in a horizontal plane. It is pos- 
itive when acting to the right for an observer facing in the 
direction of travel. C is measured in pounds. 

db. Decibel, measure of sound pressure level above unit 
pressure. 

Depth Charges. Projectiles used to attack subsurface targets. 

Directivity Index. A measure of the directional properties of 
a transducer. It is the ratio, in decibels, of the average in- 
tensity, or response, over the whole sphere surrounding the 
projector, or hydrophone, to the intensity, or response, on 
the acoustic axis. 

Dispersion. In ballistics, the scattering of shots about the 
target. 

Drag, D. The force exerted on the projectile parallel with the 
direction of motion. It is positive when acting in a direction 
opposite to the motion, D is measured in pounds. 

e. CP eccentricity, expressed as decimal fraction of length of 
projectile. 

Fineness or Slenderness Ratio. The ratio of the length to 
the maximum diameter of a projectile. 

g. Acceleration due to gravity (feet per second). 

GT. A crystal showing a zero temperature coefficient over a 
very wide range of temperature — the frequency variation is 
less than 1 part in 1,000,000 throughout a temperature 
range of 100 degrees centigrade. 

H. Hull moment (foot-pounds). 

fiB- Pressure in the bubble (feet of water). 

h L- Pressure in the undisturbed liquid, submergence plus baro- 
metric head (feet of water). 

HVAR. High-velocity aircraft rocket. 

Hydrophone. An underwater microphone. 

Incipient Cavitation. Generally, cavitation developed to the 
point where it may first be seen as a steady phenomenon. 
Sometimes, when so stated, the point at which the noise 
produced begins to increase from this cause. 

IsopiESTic Surface. A surface over which the pressure is 
constant. 

JouKOWSKi Streamlined Shapes. A family of airfoil sections 
derived from a circle by a mapping function invented by 
N. Joukowski. 




281 


282 


GLOSSARY 


K. Cavitation parameter. 

Karman Trail. The wake trailing certain two-dimensional 
bodies and consisting of vortices shed alternately from op- 
posite sides of the body. 

Ki. K value for incipient cavitation. 

Kinematic Viscosity, v. The ratio of absolute viscosity to the 
density. 

. Overall length of projectile (feet). 

l/d. Fineness or slenderness ratio. 

Laminar Flow. The type of flow in which there are no local 
velocity fluctuations so that each fluid layer slips smoothly 
over layers nearer the projectile. 

Lattice Effect. As used herein, refers to modifications of the 
velocities and pressures around a single vane or airfoil in a 
lattice or row of vanes, compared to the velocities and pres- 
sures when the vane is alone in an infinite body of fluid. 

Lift. Force exerted on a projectile normal to the direction of 
motion and in a vertical plane. It is positive when acting 
upward. Lift is measured in pounds. 

M. Moment (foot-pounds). 

Ma c.. Pitching moment per unit length of hydrofoil span, 
measured about a.c. (foot-pounds). 

Meg. Moment about CG (foot-pounds). 

N. Normal component (pounds). 

Nose. The curved portion of the projectile forward of the 
cylindrical main section. 

Pb- Vapor pressure in entrance bubble, corresponding to the 
water temperature (pounds per square foot). 

Pl- Absolute pressure in undisturbed liquid (pounds per 
square foot). 

Pitch Angle, a. The angle in a vertical plane between the 
projectile axis and the direction of motion. It is positive for 
nose-up positions. 


R. Reynolds number. 

p. Mass density of fluid (slugs per cubic foot). 

Sonic Frequencies. Range of audible frequencies, sometimes 
taken as from 0.02 kc to 15 kc. 

Sonic Velocity. The velocity of sound in air, about 1,100 fps 
(750 mph). 

Subsonic Velocities. Velocities below the sonic velocity. 

Supersonic Frequencies. Range of frequencies higher than 
sonic. Sometimes referred to as ultrasonic to avoid confusion 
with growing use of the term supersonic to denote higher- 
than-sound velocities. 

Supersonic Velocities. Velocities above the sonic velocity. 

SSR. Spin-stabilized rocket. 

Tail. The fin, or fins, and ring structure with supporting parts 
at the aft end of the projectile. It includes rudders, if any. 

Turbulent Flow. That type of flow in which there are 
irregular fluctuations distinct from vortex motion in general. 
It results in continuous interchange of particles between 
streamlines with different velocities. 

V. Mean relative velocity between water and projectile (ft per 

sec). 

Viscosity, p. The fluid property which resists relative motion 
between adjacent sections, often called absolute viscosity. 
See also kinematic viscosity. 

IF. Specific weight of fluid (lb per cu ft). 

Whip. The change at water entry in the angular velocity of 
the projectile in the vertical plane. 

Yaw' Angle, \p. The angle, in a horizontal plane, betw een the 
projectile axis and the direction of motion. It is positive 
when clockwise as viewed from above. 



BIBLIOGRAPHY 


Numbers such as Div. 6-712-M2 indicate that the document listed has been microfilmed and that its title appears in the 
microfilm index printed in a separate volume. For access to the index volume and to the microfilm, consult the Army or Navy 
agency listed on the reverse of the half-title page. 


1. Measurements of the High Frequency Noise Produced by 
Caviiating Projectiles in the High Speed Water Tunnel^ 
Robert T. Knapp, NDRC 6.1-sr207-924, Hydrodynamics 
Laboratory, Aug. 31, 1943. 

2. CavUation Noise from Umlerwater Projectiles, James W. 
Daily and Howard Bailer, NDRC 6.1-sr207-1910, Hydro- 
dynamics Laboratory, Mar. 21, 1945. 

3. Flon Diagrams of Projectile Components, Robert T. Knapp, 
Garrett Van Pelt, and Elizabeth A. Thorne, NDRC 

6.1- sr207-1649, HML Report ND-3C, CIT, Sept. 15, 1944. 

Div. 6-712-M2 

4. Underwater Behavior of 3.5'' Aircraft Rockets, I. S. Bowen, 
JBC 23, CIT, Dec. 6, 1943. 

5. Fluid Mechanics for Hydraulic Engineers, Hunter Rouse, 
McGraw-Hill Book Company, New York, 1938. 

5a. Ibid., p. 228. 

5b. Ibid., p. 248. 

5c. Ibid., p. 251. 

6. Modern Developments in Fluid Mechanics, Vols. I and II, 
edited by S. Goldstein, Oxford University Press, 1938. 

7. Aerodyrmmic Theory, Vols. I to VI, edited by W. F. 
Durand, Julius Springer, Berlin, 1934. 

7a. Vol. I, Div. C, Chap. III. 

7b. Vol. VI, Div. Q, Sec. 9. 

7c. Vol. II, Chap. 11. 

8. Applied Hydro- ami Aeromechanics, L. Prandtl and O. G. 
Tietjens, McGraw-Hill Book Company, New York, 1934. 

9. The High Speed Water Tunnel at the California Institute of 
Technology, Robert T. Knapp, Vito A. Vanoni, and James 
VV. Daily, OEMsr-207, CIT, June 29, 1942. 

Div. 6-71 1-Ml 

10. Entrance and Cavitation Bubbles, Robert T. Knapp and 

Harold L. Doolittle, HML Report ND-31, NDRC 6.1- 
sr207-1900, Dec. 27, 1944. Div. 6-712-M3 

11. Centrifugal Pump Performance as Affected by Design Fea- 
tures, Robert T. Knapp, Trans. A.S.M.E., Vol. 63, 1941, 
pp. 251-260. 

12. Experimental Investigations of Design and Operating Fea- 
tures of Centrifugal Pumps with Reference to the Grand 
Coulee Irrigation Project, Part II, a report submitted by 
the Hydraulic Machinery Laboratory of the California 
Institute of Technology to the U. S. Bureau of Reclama- 
tion, 1942. 

• 13. Cavitation Tests on a Systematic Series of Torpedo Heads, 
NDRC Nos. 6.1-srl353-2191, Feb. 28, 1945, Hemispher- 
ical Head; 6. 1-sr 1353-2 192, Mar. 5, 1945, Blunt Head; 

6.1- srl353-2195, Mar. 21, 1945, [The] 1-Caliber Ogival 


Head; 6. 1-sr 1353-2 196, Mar. 26, 1945, [The] 2-Caliber 
Ogival Head; Hunter Rouse, John S. McNown, and 
En-Yun-Hsu, State University of Iowa. 

Div. 6-712-M5, M6, M8, M9 

14. Further Experiments on the Flow Around a Circular Cylin- 
der, ARC Reports and Memoranda 1369, A. Fage and 
V. M. Faulkner, February 1931. 

15. An Investigation of Fluid Flow in Two Dimensions, ARC 
Reports and Memoranda 1194, A. Thom, November 1928. 

16. Torpedo Launching Project Report for Year Ending Novem- 

ber 30, 19Uy F. C. Lindvall, OSRD 2346, Report CIT/ 
JHC-5, CIT, Feb. 1, 1945. Div. 6-700-Ml 

17. Underwater Trajectories and Ricochet Tendencies of Rockets, 
I. S. Bowen, Proceedings of the Second Conference on 
Underwater Ballistics, January 29-31, p. 39. 

18. Measurements on Cll-Al Hydrophone with an Ellipsoidal 

and Spherical Reflector, Report C-64, OEMsr-30, UCDWR, 
Oct. 30, 1944. Div. 6-713-M3 

19. Experimental and Theoretical Investigation of Cavitation in 
Water, J. Ackeret, Report of the Kaiser Wilhelm Institute 
fiir Stromungsforchung, Gottingen, Tech., Meehan., und 
Thermodynamik, Vol. 1, January 1930, pp. 1-22. 

20. Application of Practical Hydrodynamics to Airship Design, 
R. H. Upson and W. A. Klikoff, NACA Report 405, 1931. 
20a. Ibid., Part III. 

21. The Aerodynamic Forces on Airship Hulls, Max M. Munk, 
NACA Report 184, 1923. 

22. Hydrodynamics, Sir Horace Lamb, Cambridge University 
Press, 1932, p. 155. 

23. Tests of 5” HVAR Projector with Fin and Ring Tails, 

Robert T. Knapp and Harold L. Doolittle, OSRD 6094, 
NDRC 61-sr207-2241, HML Report ND-37, CIT, Aug. 
20, 1945. Div. 6-722.6-M2 

24. Water Tunnel Tests of the 60-mm Mortar Projectile, Robert 
T. Knapp, OSRD 1869, NDRC 6.1-sr207-926, HML 
Report ND-2C, CIT, Sept. 2, 1943. Div. 6-713-M2 

25. Water Tunnel Tests of a Rocket Projectile, Robert T. 

Knapp, NDRC 6.1-sr207-1312, HML Report ND-12, 
CIT, Feb. 22, 1943. Div. 6-722.5-Ml 

26. Water Tunnel Tests of the 1^.5" Rocket Projectile with Three 

Different Fin Tails and with One Ring-Type Tail, Robert 
T. Knapp, NDRC 6.1-sr207-1304, HML Report ND-12.1, 
CIT, May 28, 1943. Div. 6-722.5-M2 

27. Water Tunnel Tests of the 7.2" Chemical Rocket, Robert T. 
Knapp and Harold L. Doolittle, NDRC 6.1-sr207-1261, 
HML Report ND-22, CIT, Dec. 22, 1943. 

Div. 6-722.7-M4 


283 


284 


BIBLIOGRAPHY 


28. Water Tunnel Tests of the Mark 13-1, Mark 13-2, and Mark 
13-2 A Torpedoes with Shroud Ring Tails, Robert T. Knapp 
and Joseph Levy, OSRD 3008, NDRC 6.1-sr207-939, 
HML Report ND-15.1, CIT, Nov. 24, 1943. 

Div. 6-721.2-M2 

29. Water Tunnel Tests of a 2.37" Rocket Projectile with Col- 

lapsible-Type Tails, Robert T. Knapp, OSRD 3193, 
NDRC 6.1-sr207-1314, HML Report ND-11.1, CIT, Jan. 
20, 1943. Div. 6-722.3-Ml 

30. Water Tunnel Tests of the M-7, 2.36" Antitank Rocket 
Showing a Comparison of Performance with a Folding Fin 
Tail, a Shroud Tail Ring, Two Hemispherical Ogive Noses 
of Different Profde and a Conical Pointed Nose, Robert T. 
Knapp, OSRD 3074, NDRC 6.1-sr207-276, HML Report 
ND-11.3, CIT, June 26, 1943. 

31. “Turbulence and Skin Friction,” Th. von Karman, Journal 
of the Aeronautical Sciences, Vol. I, No. 1, January 1934. 

32. Hydraulics, R. L. Daugherty, McGraw-Hill Book Com- 
pany, New York, 1937, p. 335. 

32a. Ibid., p. 205. 

33. Analysis of Ship Turning and Steering with Statement of 
Theory, members of the staff and Dr. L. 1. Schiff, Experi- 
mental Towing Tank, Stevens Institute of Technology, 
Hoboken, New Jersey, prepared for DTMB under Con- 
tract bs 22087. 

34. Force and Cavitation Tests, Mark 14-1 and Mark 15-1 Tor- 

pedoes, Robert T. Knapp and Joseph Levy, OSRD 5474, 
NDRC 6.1-sr207-2238, HML Report ND-18, CIT, July 
15, 1945. Div. 6-721.3-Ml 

35. Tests of the Mark 13-1 Torpedo with Various Noses, Robert 
T. Knapp and Harold L. Doolittle, OSRD 4765, NDRC 

6.1- sr207-1909, HML Report 15.4, CIT, Feb. 1, 1945. 

Div. 6-721.2-M7 

36. Air Propellers in Yaw, E. P. Leslie, G. F. Worley, and S. 
Moy, NACA Report 597, 1937. 

37. Water Tunnel Tests of the Mark 13-1, Mark 13-2, and Mark 
13-2 A Torpedoes, Robert T. Knapp, OSRD 2060, NDRC 

6.1- sr207-936, HML Report ND-15, CIT, Nov. 9, 1943. 

Div. 6-721.2-Ml 

38. Water Tunnel Tests of the Mark 13 Torpedo with Spade and 
Stabilizer Ring Noses, Harold L. Doolittle, HML Report 
ND-15.2, Hydrodynamics Laboratory, CIT, June 5, 1944. 

Div. 6-721.2-M3 

39. Pressure Distribution Measurements on the Mark 13-1, 13-2, 

and 13-2 A Torpedoes, Robert T. Knapp and Joseph Levy, 
OSRD 3935, NDRC 6.1-sr207-1643, HML Report ND- 
15.3, CIT, June 23, 1944. Div. 6-721. 2-M4 

40. Underwater Performance Characteristics of the Mark 13-2 A 

Torpedo with Suspension Fittings, Robert T. Knapp and 
Joseph Levy, OSRD 4096, NDRC 6.1-sr207-1650, HML 
Report 15.5, CIT, Aug. 18, 1944. Div. 6-721. 2-M5 

41. Pressure Distribution on the Mark 13 Series Torpedoes with 

Shroud Ring Tails, Robert T. Knapp and Joseph Levy, 
NDRC 6.1-sr207-1905, HML Report ND-15.6, CIT, Jan. 
15, 1945. Div. 6-721.2-M6 


42. Force Tests of Mark 13-1 Torpedo with Suspension Bands, 

Robert T. Knapp and Gerald B. Robison, NDRC 6.1- 
sr207-2231, HML Report ND-15.7, Hydrodynamics La- 
boratory, CIT, May 17, 1945. Div. 6-721. 2-M8 

43. Water Tunnel Tests of the Mark 25 Torpedo with Gas 

Exhaust through a Vertical Fin, Robert T. Knapp and 
Harold L. Doolittle, OSRD 3664, NDRC 6.1-sr207-1275, 
HML Report ND-30, Service Project NO-176, CIT, May 
8, 1944. Div. 6-721.4-Ml 

44. Water Tunnel Tests of the Mark 25 Torpedo with a Gas 

Exhaust through a Horizontal Pipe, Robert T. Knapp and 
Harold L. Doolittle, NDRC 6.1-sr207-1640, HML Report 
ND-30.1, CIT, June 5, 1944. Div. 6-721.4-M2 

45. Water Tunnel Tests of the Mark 25 Torpedo with Expanding 

Exhaust Pipe, Robert T. Knapp and Harold L. Doolittle, 
NDRC 6.1-sr207-1642, HML Report ND-30.2, CIT, June 
20, 1944. Div. 6-721.4-M3 

46. Mark 25 Torpedo Exhaust Gas Investigation, Robert T. 
Knapp and Harold L. Doolittle, OSRD 5119, NDRC 

6.1- sr207-1916, HML Report ND-30.4, CIT, Apr. 12, 

1945. Div. 6-721.4-M4 

47. Mark 25 Torpedo with Various Exhaust Pipes, Robert T. 
Knapp and Harold L. Doolittle, OSRD 5381, NDRC 

6.1- sr207-2236, HML Report ND-30.3, CIT, July 14, 

1945. Div. 6-721. 4-M5 

48. Pressure Distribution Measurements on the Mark 25 Tor- 

pedo, Robert T. Knapp and Joseph Levy, OSRD 6313, 
NDRC 6.1-sr207-2248, HML Report ND-30.5, CIT, Aug. 
31, 1945. Div. 6-721.4-M6 

49. Pressure Distribution Measurements on the Mark 14-1 and 
Mark 15-1 Torpedoes, Robert T. Knapp and Joseph Levy, 
OSRD 6092, NDRC 6.1-sr207-2244, HML Report ND- 

18.1, CIT, Aug. 15, 1945. Div. 6-721.3-M2 

50. Force and Cavitation Tests of the Mark 26 Torpedo, Robert 
T. Knapp and Robert M. Peabody, OSRD 6423, NDRC 

6.1- sr207-2249, HML Report ND-38, CIT, Aug. 31, 1945. 

Div. 6-721.3-M3 

51. Water Tunnel Tests of the Hydrobomb, Robert T. Knapp 
and Harold L. Doolittle, NDRC 6.1-sr207-1276, HML 
Report ND-29, CIT, May 13, 1944. Div. 6-723-M2 

52. Force and Cavitation Tests of the Westinghouse Hydrobomb, 

Robert T. Knapp and Robert M. Peabody, OSRD 5368, 
NDRC 6.1-81-207-2234, HML Report ND-40, CIT, June 
27, 1945. Div. 6-723-M3 

53. Force Tests of the United Shoe Machinery Corporation No. S 
Hydrobomb, Robert T. Knapp and Gerald B. Robison, 
OSRD 6093, NDRC 6.1-sr207-2247, HML Report ND- 

29. 1, CIT, Aug. 25, 1945. Div. 6-723-M5 

54. Development of the High S peed Water Tunnel and Summary 
of Results, NDRC 6.1-sr207-2351. CIT, Aug. 31, 1945. 

Div. 6-71 1-M2 

55. Analysis of Aircraft Launchings of Torpedoes Equipped 
with Shroud Rings, K. H. Keller, M. Gimprich, and W. H. 
Wilson, NDRC 6.1-srl 131-1887, Columbia University 
Special Studies Group, Mar. 26, 1945. 


BIBLIOGRAPHY 


285 


56. Water Tunnel Tests of the Antiaircraft Projectile, 
Robert T. Knapp and James W. Daily, NDRC 6.1-sr207- 
927, HML Report ND-13.1, CIT, Dec. 28, 1943. 

Div. 6-722. 1-M2 

57. Water T unriel Tests of a 2.37" Rocket Projectile with Hem- 

ispherical Noses and Ring Tails, Robert T. Knapp, OSRD 
3068, NDRC 6.1-sr207-1303, HML Report ND-11.2, 
CIT, Feb. 19, 1943. Div. 6-722.3-M2 

58. Water Tunnel Tests of the M-6, 2.36" Antitank Rocket 

Showing Comparison of Performance with the Conical 
Pointed Nose Combined with Three Types of Shroud Ring 
Tail and with Shroiid Rings of VarioiLS Lengths, Robert T. 
Knapp, NDRC 6.1-sr207-920, HML Report ND-11.4, 
CIT, July 20, 1943. Div. 6-722.2-M2 

59. Water Tunnel Tests of the M-6, 2.36" Antitank Rocket with 

Five Designs of Shroud Ring Tail, Robert T. Knapp, 
OSRD 3003, NDRC 6.1-sr207-934, HML Report ND- 
11.5, CIT, Nov. 4, 1943. Div. 6-722.2-M3 

60. Water Tunnel Tests of the 3.5" Rotating Rocket, Robert T. 
Knapp and Harold L. Doolittle, NDRC 6.1-sr207-1270, 
HML Report ND-27, CIT, Apr. 21, 1944. 

Div. 6-722.4-Ml 

61. 3.5" Rotating Rocket Tests with Various After-bodies, Rob- 
ert T. Knapp and Harold L. Doolittle, NDRC 6.1-sr207- 
1903, HML Report 27.1, CIT, Jan. 4, 1945. 

Div. 6-722.4-M2 

62. Water Tunnel Tests of the 15-cm German Spinner Rocket, 

Robert T. Knapp, NDRC 6.1-sr207-932, HML Report 
ND-23, CIT, Nov. 11, 1943. Div. 6-722.7-M3 

63. Elements of Ordnance, Col. Thomas J. Hayes, John Wiley 
and Sons, Inc., New York, 1938. 

64. Force Tests of the 1^.5" Rocket, T-38E3, Robert T. Knapp 
and Gerald B. Robison, OSRD 5113, NDRC 6.1-sr207- 
1919, HML Report ND-41, CIT, May 1, 1945. 

Div. 6-722.5-M3 

65. Tests of Four Models of the 5" SSR Rotating Rocket, Robert 
T. Knapp and Harold L. Doolittle, OSRD 5473, NDRC 

6.1-sr207-2239, HML Report ND-33, CIT, July 24, 1945. 

Div. 6-722.6- Ml 

66. Memorandum on Water Tunnel Tests of the AN MK 4i 
Bomb, Robert T. Knapp, NDRC 6.1-sr207-735, Mar. 3, 
1943. 

67. Water Tunnel Tests of the British Squid Projectile, Type C, 

Robert T. Knapp, NDRC 6.1-sr207-933, HML Report 
ND-24, CIT, Oct. 29, 1943. Div. 6-721. 5-Ml 


68. Water Tunnel Tests of the British Squid Projectile, Type C, 

with Two Alternate Flat Noses, Robert T. Knapp and 
Harold L. Doolittle, NDRC 6.1-sr207-938, HML Report 
ND-24.1, CIT, Nov. 29, 1943. Div. 6-721.5-M2 

69. Drag Tests of the British Squid, Robert T. Knapp and 

Gerald B. Robison, NDRC 6.1-sr207-1904, HML Report 
ND-24.2, CIT, Jan. 8, 1945. Div. 6-721. 5-M3 

70. Force Tests of the Squid with New Afterbody, Tails, and 

Noses, Robert T. Knapp and Gerald B. Robison, OSRD 
5529, NDRC 6.1-sr207-2243, HML Report ND-24.3, 
CIT, July 30, 1945. Div. 6-721. 5-M4 

71. Tests of the AN-Mark 53 Aircraft Depth Bomb, Robert T. 
Knapp and Harold L. Doolittle, OSRD 6091, NDRC 

6.1- sr207-2350, HML Report ND-44, CIT, Aug. 31, 1945 

Div. 6-723-M6 

72. Force Tests of Concrete Practice Bombs, M38A2 Practice 

Bomb, AN-M43 General Purpose 500-lb Bomb, AN-M56 
LC 4000-lb Bomb, Robert T. Knapp and Robert M. Pea- 
body, OSRD 5757, NDRC 6.1-sr207-2245, HML Report 
ND-32, CIT, Aug. 14, 1945. Div. 6-723-M4 

73. Dynamic Stability of Bombs and Projectiles, M. A. Biot, 
NDRC 3.2-sr418, CIT, Sept. 6, 1943. 

74. Force and Cavitation Characteristics of the NACA-44i^ 
Hydrofoil, Robert T. Knapp and James W. Daily, NDRC 

6.1- sr207-1273, HML Report ND-19, CIT, June 10, 1944. 

Div. 6-712-Ml 

75. The Characteristics of 78 Related Airfoil Sections frorn Tests 
in the Variable Density Wind Tunnel, E. N. Jacobs, K. E. 
Ward, and R. M. Pinkerton, NACA T. R. No. 460, 1933. 

76. Calculated and Measured Pressure Distributions over the 
Midspan Section of the NACA 4412 Airfoil, R. M. Pinker- 
ton, NACA T. R. No. 563, 1936. 

77. Airfoil Section Characteristics as Affected by Variations of 
the Reynolds Number, E. N. Jacobs and A. Sherman, 
NACA T. R. No. 586, 1937. 

78. Airfoil Section Data Obtained in the NACA Variable- 
Density Tunnel as Affected by Support Interference and 
Other Corrections, E. N. Jacobs and I. H. Abbott, NACA 
T. R. No. 669, 1939. 

79. Aerodynamics of the Airplane, C. B. Millikan, Wiley, 1941. 

80. Determination of the Characteristics of Tapered Wings, 
R. F. Anderson, NACA T. R. No. 572, 1936. 

81. The Design of Propeller Pumps and Fans, M. P. O’Brien 
and R. G. Folsom, University of California, Publication in 
Engr. Vol. 4, No. 1, University of California Press, 1939. 


CONTRACT NUMBERS, CONTRACTORS, AND SUBJECT OF CONTRACT 


Contract 

Numbers 

Name and Address 
of Contractor 

Subject 

OEMsr-20 

The Trustees of Columbia University in the 
City of New York 

New York, N. Y. 

Studies and experimental investigations in con- 
nection with and for the development of equip- 
ment and methods pertaining to submarine 
warfare. 

OEMsr-1128 

The Trustees of Columbia University in the 
City of New York 

New York, N. Y. 

Conduct studies and experimental investigations 
in connection with and for the development of 
equipment and methods involved in submarine 
and subsurface warfare. 

OEMsr-207 

California Institute of Technology 

Pasadena, California 

Construction and operation of a high speed water 
tunnel, and use of such water tunnel in research 
and experimental investigations involving un- 
derwater projectiles and detection equipment. 

OEMsr-1353 

The Iowa Institute of Hydraulic Research of 
the University of Iowa 

Iowa City, Iowa 

Conduct studies, experimental investigations, ob- 
servations, and tests of pressure distribution 
about underwater structures of varying form, 
together with photographic records of the char- 
acter of the flow, especially with reference to the 
onset and continuance of the phenomena of 
cavitation, all at varying speeds and under 
selected conditions of operations. 


286 


SERVICE PROJECT NUMBERS 


The projects listed below were transmitted to the Executive Secretary, 
NDRC, from the War or Navy Department through either the War 
Department Liaison Officer for NDRC or the Office of Research and 
Inventions (formerly the Coordinator of Research and Development), 
Navy Department. 


Service 

Project 

Number 


Subject 


OD-99 


NO-141 


NO-176 


Hydrodynamic characteristics of projectile forms 
Torpedoes for high speed aircraft 

Determination of the dynamic characteristics of specified bomb and projectile shapes . 


NS-294 


Cavitation research 


287 


.ir, I .. .. J ■: • 



y ■ . “^ - • . >'* 

*•'*• • \ ■%^/^**' ' 
^ * • ' w 





■j'- .- 'k f.' ,.-. 

^ .''A 



» I I f • " . 

.V- • V * J' •• 1 

sir ^ 

£L^ V. .; , • t - 

:!??■'<':■■ ' 

^ 4Li w 5T • 







Mr ''^-jr :^. 

W .N*,'- :;^\r* ■ * 



y-rmPL*^ - • -w * > # 

V ''T “t 




v«- 






■ 

•..?,>- , t *^* -* '«r-; , r» , . b’ 

,- •< .-'J ^ 3 / .lA. H 

' -vj, ■. ■■ 



t <^-.*1^ '^y 

' '.A • 




- y^r- '" 

4 '> ' i .'Xv , \y 

cT ■^- ' ^ 


:i^' / •' 'K ■'*K'?'«-- j!* 

in’ ■■.,,'•■ - i' 

r . . T «. i »• * tk. Ik 


'S' if'-:'* c 


WiM '’"V' ■ ~ ■ ' 


^V:>V;rii’^',%''',,'"}l‘^- / .v: '■/'.//^t'^' 




v>y 


. /..'tfcL I 


INDEX 


The subject indexes of all STR volumes are combined in a master index printed in a separate volume. 
For access to the index volume consult the Army or Navy Agency listed on the reverse of the half-title page. 


A A rocket, 2)^ inch, 234 
ADP hydrophone (ammonium dihydro- 
gen phosphate), 64 

Aerodynamics, terms and symbols, 260- 
261 

Afterbody 

see Projectile afterbody 
Air bombs, 253-258 
effect of asymmetry, 253-256 
hydrodynamic characteristics, 253, 
256 

physical dimensions, 254 
types, 253-256 
Air bubble formation 

see Bubbles, entrance; Cavitation, 
bubble formation 

Air separator, free-surface water tun- 
nel, 53-56 

Aircraft torpedoes. 203-207 
dimensions, 203 

hydrobombs, 203, 205-207, 214, 217, 
225 

Mark 13 series, 135, 178, 203, 226- 
220 

Mark 25; 203, 205, 222 
trajectory, 3 
water-entry studies, 200 
Air-launched projectiles 
nose shapes, 73-75, 77 
trajectory, 4 

water-entry studies, 201-202, 200 
AN-M43 air bomb, 253-256 

hydrodynamic characteristics, 253, 
256 

physical dimensions, 254 
AN-M56 air bomb, 253-256 
hydrodynamic characteristics, 256 
physical dimensions, 254 
AN Mark 41 depth charge 
effect of nose shape on drag force, 188 
hydrodynamic characteristics, 248- 
249 

physical characteristics, 246 
AN Mark 53 depth charge, 251-252 
Artillery projectiles, nose shapes, 71-73 
Ashcan (depth charge), 1 
A.spect ratio, hydrofoils, 259-263 
.\X 90 hydrophone, 64 

Bazooka (rocket), 235-237 
collapsible fin tails, 235 
forceand moment coefficients, 235-236 
ring tails, 236-237 
Bentonite, use in flumes, 2 
characteristics, 27 
purification, 34 


sensitivity to mineral content of wa- 
ter, 33 

streaming double refraction, 33-34 
Bernoulli equation, conservation of en- 
ergy, 98 
Bombs, air 
see Air bombs 

British Squid (depth charge), 249-251 
drag coefficient, 189-190 
physical characteristics, 246 
Bubbles, cavitation 

see Cavitation, bubble formation 
Bubbles, entrance, 96-97, 107-111 
comparison with cavitation bubbles, 
107-108 
cross force, 110 
decay, 109 

desirable characteristics, 115 
effect of nose shape, 115-116 
equilibrium yaw angles within bub- 
ble, 110-111 
formation, 108-109 
maximum diameter, 109 
projectile entrance velocity, 109 
significance of bubble shapes, 109- 
110 

California Institute of Technology, 1 
Cameras for hydrodynamic studies, 44, 
56-60 

Cavitation, 96-117 

coarse-grained, 103, 119, 121 
definition, 96, 98 
degrees of cavitation, 101-103 
desirable characteristics, 113-115 
effect of projectile nose shape, 116, 
126 

effect on projectile trajectory, 104- 
105, 109-111 

effect on projectile yaw, 1 10-111, 123- 
129, 136-137 

fine-grained, 103, 119-122 
formula for velocity, 101 
gas cycles, 105-107 
location of point of inception, 98-100 
parameter, 100-101, 118, 261, 276, 
278-279 

photography, 119, 127-133, 266 
projectile nose cavitation, 111-133 
projectile resistance, 100 
sources, 99 

tests, 11, 22-23, 26-27, 62-63 
torpedoes, 136, 152-153, 224-226 
types, 103-104, 119-122, 159-160 
Cavitation, bubble formation, 107-111 
see also Bubbles, entrance 


comparison with entrance bubbles, 
107-108 

conclusions from studies, 133 
cross force, 110 
desirable characteristics, 115 
effect of projectile nose shapes, 131- 
133 

equilibrium yaw angles within bub- 
ble, 110-111 
hydrofoils, 265-270 
location on projectile nose, 119 
physical dimensions from photo- 
graphs, 127-130 

significance of bubble shapes, 109- 
110 

Cavitation, effect on hydrodynamic 
forces, 134-154 

air- water entry of projectiles, 153 
conclusions from studies, 151-154 
cross force and moment, 147-151 
drag, 134-147 
hydraulic machinery, 154 
lifting surfaces, 153 
torpedoes, 152-153 
Cavitation noise, 155-170 
background noise, 156-159 
body shape, 159 

correlation with growth of cavita- 
tion, 159-160 

frequency distribution, 169-170 
location of noise source, 167-169 
magnitude, 166, 169 
measuring apparatus, 62-63, 155-156 
sound pressure and bubble collapse, 
165 

sound pressure versus cavitation 
growth, 160-165 
surface conditions, 165 
velocity of projectiles, 165-166 
visible cavitation and the noise 
source, 167 
Cavity drag, 140-147 

comparison with calculated drag, 
146-147 

cross forces, 147 

description of cavity, 141-143, 146 
drag versus cavitation parameter, 
144, 146 

effect of body shape, 141-144 
form drag formula, 140-141 
noncavitating drag, 147 
of a cylinder, 144-147 
wall effects, 147 

Cavity formed by water entry of pro- 
jectile 

see Bubbles, entrance 


289 


290 


INDEX 


Chemical rocket, 7.2 inch, 230 
Controlled-atmosphere launching tank 
see Launching tank for projectiles 
Cross force 
definition, 185, 275 
effect of projectile components, 192 
formula, 185 
influence of yaw, 192 
Cross force, effect of cavitation, 110, 
111, 147-151 

cavity symmetry versus nose shape, 
147-148 

conclusions from studies, 151-153 
description of cavities, 149-150 
measured coefficients, 148-151 
Cross force coefficient of projectiles 
see under name of projectile 
Crystals, use in producing light paths, 
30-33 

bentonite, 33-34 
requirements, 30-33 
tobacco mosaic virus, 34 

Damping force, 193-195 
coefficients, 194-195 
definition, 193 

effect of projectile components, 199- 
200 

mechanics of damping, 193-194 
theoretical force distribution, 193 
Data analyzer, 37-38, 51-52 
Depth and roll recorder, 223-224 
Depth charges, 1, 245-252 
7 inch, 240-241, 246 
afterbody shape, 82 
air-launched, 77 
Ashcan, 1 

blunt nose shape, 136 
British Squid, 189-190, 249-251 
design requirements, 245 
general features, 245 
hydrodynamic tests, 245 
Mark 41; 188, 246, 248-249 
Mark 53; 251-252 
methods of launching, 245 
mousetrap, 245-246 
New London, 245-246 
small-charge group, 246-248 
yaw angle tests, 246 
Differential pressure gauge, 21 
‘ Drag, 186-192 

definition, 185, 275 
form drag, 186, 187 
formula, 140-141, 185, 188 
in relation to flow, 187 
influence of yaw, 192 
skin-friction, 137-140, 186-187, 189 
total drag coefficient, 186 
variation with Reynolds number, 
215-216 

Drag, effect of cavitation, 110, 134-147 


blunt-nosed bodies, 136, 139 
cavitation parameter, 144, 146 
cavity drag, 140-147 
conclusions from studies, 151-152 
effect of yaw, 136-137 
effect on boundary layer and skin 
friction, 137-140 

hemisphere projectile nose, 134-135 
separation of flow, 137-139 
square-end cylinder projectile nose, 
135 

torpedo noses, 135-136 
Drag, effect of projectile components, 
188-192 

body, afterbody, and tail, 189-192 
effect of ring tail, 228, 236-237 
nose shape, 188-192, 248 
Drag coefficient of projectiles 
see under name of 'projectile 
DRR (depth and roll recorder), 223-224 
Dynamic stability of projectiles 
see Projectile stability 
Dynamometer for high-speed water 
tunnel, 12 


Eyrite 

see M. S. Eyrite 

15-cm German spinner rocket, 

239, 241-242 

Pintails, projectiles, 175-181, 232-233 
collapsible, 183-184, 232, 235 
comparison with ring tails, 175-176 
184, 232 

effectiveness, 178 

fixed fins, 176-177 

influence of body interference, 176 

moment, 176-177 

rockets, 84-85, 183-184, 235 

torpedoes, 85 

5-inch HVAR rocket, 230-232 
5-inch SSR rotating rocket, 243 
Flow diagrams of projectile, 69-95 
60-mm mortar, 238 
afterbodies, 79-83 
application to projectile design, 93 
nose shapes, 69-79 
rocket booms, 80, 89-90 
tails, 83-92 

Flow studies, equipment 
see Polarized light flume 
Flume, polarized light 
see Polarized light flume 
Force measuring equipment, 9, 16-18 
Forces on projectile bodies ' 
see Hydrodynamic forces 
Form drag 
cause, 186 
coefficient, 187 
effect of projectile tail, 189 
formula, 140-141 


projectile nose shape, 190-192 
43^ inch non-rotating rocket, 232-234 
4:]/2 inch rotating rocket, 242 
Free-surface water tunnel, 52-56 
air separator, 53-56 
comparison with polarized light 
flume, 27 
purpose, 5-6 
working section, 53 

Gauges 

see Pressure gauges 
German spinner rocket, 15-cm, 

239, 241-242 

Gorton pantograph machine, 67 
Guns, fluid friction losses in barrel, 271- 
273 

friction factor, 271 
relation to smooth tubes, 273 
test results, 271-273 

Hayes, stability requirement for spin- 
ning projectiles, 242 
High-speed water tunnel 
see Water tunnel, high-speed 
Hydraulic machinery, effect of cavita- 
tion, 154 

Hydraulic Machinery Laboratory, 1 
Hydrobombs (jet-propelled torpedoes) 
cavitation, 225, 226 
dimensions, 203 

lift and pitching curves, 211-214 
moment coefficient, 214 
power, 217 

United Shoe Machinery Corpoi ation, 
206-207 

Westinghouse, 205-207 
Hydrodynamic forces, 171-174 
see also Lift force 
cross force, 147-151, 185, 192 
damping, 193-195, 199-200 
distributed and resultant forces, 171- 
173 

drag, 134-147, 186-192 
dynamic stability, 195-200 
ideal fluid, 171-172 
moment, 172-183 
nose cavitation, 134-137 
real fluid, 172 
ring tail, 178, 228, 236-237 
theoretical moment, 173 
yaw, 192 

Hydrodynamics, CIT laboratory, 1-6 
equipment, 4-6 
history, 1-3 

Hydrodynamics, laboratory apparatus, 
7-68 

controlled-atmosphere launching 
tanks, 5, 35-52 
electrical accessories, 61-62 
free-surface water tunnel, 52-56 


A L - j 


INDEX 


291 


high-speed water tunnel, 4, 7-27 
hydrophones, 62, 64 
photographic equipment, 42-51, 56- 
61 

polarized light flume, 1, 5, 27-35 
shop facilities, 66-68 
sound-measuring equipment, 62-65 
Hydrodynamics, tests, 25-27 

cavitation, 11, 22-23, 26-27, 62-63 
depth charges, 245-246 
force, 25 

powered model and exhaust tests, 27 
pressure distribution, 26 
speed, 26 

Hydrofoil tests, 259-270 
cavitation, 265-270 
dimensions of hydrofoil, 259 
hydrodynamics, 261 
infinite aspect ratio, 259-263 
installation, 259 

Reynolds number and turbulence, 
265 

theoretical characteristics, 263 
tunnel wall interference, 263 
wind tunnel measurements, 263-265, 
269 

Hydrophones for hydrodynamic stud- 
ies, 62, 64 
ADP, 64 
AX 90; 64 

free-field calibrations, 64 

Jet-propelled torpedoes 
see Hydrobombs 

Karman trail (wake trailing), 147, 216 
Kopf stabilizing ring, 75-77 

Launching tank for projectiles, 5, 

35-52 

atmospheric pressure, 35-36 
design specifications, 37 
density of air, 36 
purpose, 2, 5, 35 
requirements, 35-36 
surface tension, 36 
variable-pressure launching tank, 2 
Launching tank for projectiles, con- 
struction, 38-52 

data analyzer system 37-38, 51-52, 
launcher, 40-42 
main tank, 38-40 
recording cameras, 44 
trajectory recording system, 42-51 
Lift force 

coefficient curves for hydrobombs, 
214 

definition, 185, 275 
effect of projectile components, 192 
Unless bodies, 193-194 
formula, 185, 261 


influence of yaw, 192 
relation to moment, 172-173 
torpedoes, 211-215 
Light flume, polarized 
see Polarized light flume 

M38A2 practice bomb, 253 
hydrodynamic characteristics, 256 
physical dimensions, 254 
Manometer, multiple differential, 21- 
22 

Mark 3 acoustic unit (amplifying sys- 
tem), 64 

Mark 13 torpedoes, 135-136, 203, 226- 
229 

cavitation, 136, 225 
dimensions, 203 
effect of ring tail, 178, 228 
modifications, 228 
moment coefficient, 178 
pitch angle and rudder setting, 219 
power, 217 
shroud-ring tail, 226 
Mark 14 torpedo, 197-198 
cavitation, 225 
dimensions, 203 
hydrodynamic properties, 198 
pitch angle and rudder setting, 219 
power, 207, 217 
pressure distribution, 220-222 
stability, 197 

Mark 15 torpedo, 203, 207, 217, 219 
dimensions, 203 
equilibrium conditions, 219 
power, 217 

pressure distribution, 221-222 
Mark 25 torpedo, 205 
dimensions, 203 
pressure distribution, 221-222 
Mark 26 torpedo, 208-209, 228-229 
cavitation, 225 
dimensions, 203 
modifications, 228 

pitch angle and rudder setting, 219 
power, 217 

Mark 41 depth charge, 248-249 
characteristics, 246 
drag force, 188 

Mark 53 depth charge, 251-252 
Massachusetts Institute of Technology, 
bentonite studies, 33 
Moment coefficient of projectiles, 261 
see also under name of projectile 
Moment of force, 172-183 
damping moment, 193-195 
effect of cavitation, 147-151 
effect of projectile fin tail, 176-177 
effect of projectile length, 182 
effect of ring tails, 178, 236-237 
evaluation of theoretical moment, 
173-174 


relation to lift, 172-173 
Mortar, 60-mm, 237-238 
flow-line drawings, 238 
force coefficient curves, 238 
physical characteristics, 237-238 
stabilizing device, 238 
Mousetrap depth charge, 245-248 
M. S. Eyrite (bentonite), use in flumes, 
2 

characteristics, 27 
purification, 34 
reaction with metals, 27 
sensitivity to mineral content of wa- 
ter, 34 

streaming double refraction, 33-34 

NACA 4412 hydrofoil 
see Hydrofoil tests 
Naval Ordnance Laboratory, 64 
New London depth charges, 245-246 
Noise from cavitating projectiles 
see Cavitation noise 
Normal force on projectile body, 171 
Nose shapes of projectiles 
see Projectile nose shapes 

Pantograph machine, 67 
Photocell 

use in pressure gauges, 19 
use in projectile launching tank, 42 
Photographic equipment for hydrody- 
namic studies, 56-61 
portable camera, 56-60 
processing facilities, 56, 60-61 
trajectory recording system, 37, 42- 
51 

Photography of cavitation, 127-133, 
266 

bubble dimension measurement, 127- 
130 

ogive projectile nose, 119 
spherogive projectile nose, 130-131 
Pitch angle, definition, 275 
Polarized light flume, 1, 5, 27-35 
applications, 29 
bentonite, 27, 33-34 
circulating pump, 27-29 
comparispn with water tunnels, 27 
construction, 27-29 
diffuser section, 29 
light source, 29 

mechanisms for studying fluid flow, 
29 

operation, 27, 35 
polarized screens, 27, 29 
streaming double refraction, 30-33 
tobacco mosaic virus, 34 
working section, 29 
Pressure distribution tests, 26 
measuring equipment, 21-22 
torpedoes, 220-222 


292 


INDEX 


Pressure gauges, 19-21 
balance sensitivities, 21 
control panel, 20 
differential pressure gauge, 21 
hydraulic transmission system, 20- 
21 

photocell control, 19 
principle of operation, 19 
sensitivity and range of system, 20 
Projectile, air-launched 
nose shapes, 73-75, 77 
trajectory, 4 

water-entry studies, 201-202, 209 
Projectile afterbody, 79-83 
booms, 80 
conical tapers, 80 
damping and stability, 199 
depth charges, 82 
drag force, 189-192 
fine afterbodies, 82 
flow diagrams, 79-83 
ogives, 79-80 
recessed, 80 
rocket nozzles, 82-83 
spherogives, 80 
torpedo, 82 
Projectile design 
finless bodies, 171-174 
flow diagrams, 93 
spherogive nose shape, 126-127 
Projectile dynamics within cavitation, 
104-105, 109-111 
.see also Cavitation 
cross force, 110, 111 
curvature of path. 111 
drag force, 110 
effect of body shape, 141-144 
effect of nose shapes, 1 1 1-117 
equilibrium yaw angles within bub- 
bles, 110-111 

significance of bubble shapes, 109- 
110 

Projectile entrance into water 
see Bubbles, entrance 
Projectile launching tank 

see Launching tank for projectiles 
Projectile nose cavitation, 1 1 1-133, 151- 
153 

bubble formation, 119, 123* 126, 131- 
133 

cavity symmetry, 147-148 
effect of sphere size, 132 
effect of yaw angle, 123-129 
effect on hydrodynamic forces, 134- 
137 

ellipsoidal nose, 112 
hemispherical nose, 112, 120-129, 
134-135 

incipient cavitation, 118 
measurements from photographs, 133 
method of testing, 118 


ogive shape, 113, 118-126, 131-133 
recommendations, 117 
resistance to cavitation, 113, 117 
selection of nose shape, 115 
spherogive shape, 126-133 
square-end cylinder, 135 
Projectile nose shapes, 69-79 
air-launched projectiles, 73-75, 77-78 
characteristics, 111-117 
conical tapers, 73 

damping and stability, 199, 240, 246- 
248 

drag force, 187-192, 248 
ellipsoids, 70, 112 
flow diagrams, 69-79 
hemispherical 75, 112 
high-velocity projectiles, 78 
Kopf ring, 75-77 

modified square-end cylinders, 77 
modified tapers, 77 
noses with common length, 78 
ogives, 71, 73-79, 113 
pickle barrel, 75 
selection of shape, 69 
spherogive, 71-73, 76, 116-117 
Projectile stability, 195-200 
criteria for stability, 195-197 
definition, 195 
dependent factors, 197 
effect of various components, 178, 
199-200 

formula, 196-197, 242 
Mark 14 torpedo, 197 
nose shape, 199, 240, 246-248 
propellers, 200 
rudders, 196 

spinning projectiles, 239, 242 
tail structure, 197, 199, 246-248 
Projectile tails, 83-92, 175-184 
body length, 176, 181-183 
damping, 199-200 
design variables, 175-184 
drag force, 189-192 
effectiveness, 175-176 
fin tails, 84-85, 175-181, 183-184, 
232-233 

flow diagrams, 83-92 
form and action, 175 
form drag, 186 
moment coefficient, 176 
non-rotating projectiles, 175-184 
operation, 83-84 
propellers, 200 
purpose, 83, 175 

ring tails, 85-92, 177-184, 226-228, 
232-237 
rudders, 192 
square tails, 92 

stability, 197, 199-200, 246-248 
Projectile trajectory recording system, 
37, 42-51 


camera drive motor, 45-47 
light source, 48-51 
magazine loader, 47 
optical coverage of cameras, 43-44 
recording speed, 44-45 
spherical windows, 42-43 
Projectile yaw 
depth charges, 245 

effect of cavitation, 110-111, 123- 
129, 136-137 

effect on hydrodynamic characteris- 
tics, 192 
torpedoes, 220 

Refraction, double, of crystals, 30-34 
bentonite, 33-34 
requirements, 30-32 
tobacco mosaic virus, 34 
Reynolds number, 185, 261, 276 
Ring tails, projectiles, 85-92, 177-184 
226-228, 232-237 
advantages, 228, 232 
body length, 177, 181-183 
boom mounting, 89-90, 177-178, 234 
comparison with fin tails, 175-176, 
184, 232 

force coefficient curves ,181 
high-drag ring tails, 92, 181 
hydrodynamic forces, 178, 228, 236- 
237 

mounted on extended fins, 90-92 
shroud ring, 226 
with exhaust stack, 92 
with ogival afterbodies, 85 
Rockets, 80-90 

collapsible fins, 84-85, 183-184 
fixed fins, 84-85 
low-velocity, 77 

moment coefficient, 178, 235-236 
nozzles, 82-83 

rings on rocket booms, 89-90 
use of booms, 80 

Rockets, non-rotating, 230-237, 239- 

241 

2^ inch AA rocket, 234 
2.36 inch rocket (bazooka), 235-237 
43^ inch rocket, 232-234 
5 inch HVAR rocket, 230-232 
7.2 inch chemical rocket, 230 
general features, 230 
hydrodynamic characteristics, 235- 
236, 239-241 

Rockets, rotating, 239-244 

3.5 inch rocket, 240-241 

4.5 inch HE rocket T38E3; 242 
5 inch SSR, 243 

15-cm German spinner rocket, 241- 

242 

general features, 239 
hydrodynamic characteristics, 239 
propellant burning, 239 




INDEX 


293 


stability, 239, 242 • 

water tunnel tests, 239 
Roll recorder for projectiles, 223-224 
7 inch depth charge, 245-246 
7.2 inch chemical rocket, 230 

Shear force on projectile body, 171 
60-mm mortar, 237-238 
flow-line drawings, 238 
force coefficient curves, 238 
physical characteristics, 237 
stabilizing devices, 238 
Skin-friction drag, 186-187, 189-192 
cause, 186 
coefficient, 186-187 
effect of cavitation, 137-140 
effect of projectile tail, 189 
formula, 186-187 
projectile body length, 189 
turbulent flow, 186 

Sound measuring equipment, hydrody- 
namic studies, 62-65 
amplifying and filtering equipment, 
64-65 

cavitation noise, 62 
free-field calibrations, 64 
hydrophone, 62 
internal receivers, 64 
sound reflectors, 63 

Sound pressure, effect of cavitation, 
160-165 

Sound reflectors for hydrodynamip^ 
studies, 63 
Specifications for 

phere launching tank 
Specifications for high-speed water 
nel,7-ll - 

balance equipment for force measure- 
ments, 9 

requirements for cavitaiipn 
11 

velocity, 8 
working section, 8-9 
Spin-stabilized rockets 
see Rockets, non-rotating 


3.5 inch rotating rocket, 240-241 
Tobacco mosaic virus, 34 
Torpedo, aircraft 

see Aircraft torpedoes 
Torpedoes, 203-229 

adjustable rudders, 85, 175 
afterbody shape, 82 
aircraft, 3, 75, 203-207 
cavitation, 136, 152-153, 224-226 
dimensions, 203 
fin tails, 85 

hydrobombs, 203-207, 214, 217, 

225 

Mark 13; 135-136, 226-229 
Mark 14; 197-198, 203, 217, 219- 
222, 225 

Mark 15; 203, 207, 217, 219, 221 
Mark 25; 203, 205, 222 
Mark 26; 208-209, 228-229 
modifications, 226-229 
nose shape, 135-136 
pitch angles and rudder settings, 
217-219 
power, 216-217 
purpose of tail, 83 
shroud-ring tail, 228 
trajectory, 3 

water-borne, 203, 207-209 
water-entry studies, 209 
Torpedoes, force measurements, 198, 
200, 209-219 

cross force coefficient, 211-215 


United Shoe Machinery Corporation, 
206-207 

Variable-pressure launching tank, 2 


controlled-atm£® re^^ffl^Es, Sj^RVlpT 

L^SiflinB^c^ 






studies. 


By 


219 

lift and moment, 211-215 
Torpedoes, pressure distributio^|f&19- 
224 

application of measured 

.DECLAS^FIED 

.1 ^ecTof component shape, 221 




ata , 


Squid (British depth charge), 249- 
251 

drag coefficient, 189-190 
physical characteristics, 246 
SSR rocket, 5 inch, 243 
Stability of projectiles 
see Projectile stability 
Streamline body, definitioo, 188 


method of measuring, 219 

O^i^rfflylMding system for pro- 
jectiles 

Defense mtaafo^oj^^^fgjr^i^gry recording 

system 


LIBBAR^O#. 4B0N^1 


T38E3 rocket, 242 || 

Tails of projectiles 
see Projectile tails 

Tank, controlled-atmosphere launching 
see Launching tank for projectiles 
Taylor Model Basin, 24 


2.36 inch rocket, 235-! 
collapsible fin tails, 235 
force and moment coefficie 
236 

ring tails, 236-237 

Underwater projectile design 
see Hydrofoil tests 


4 


Water entry of projectiles 
see Bubbles, entrance 
Water tunnel, 155-159 
see also Hydrofoil tests 
background noise, 156-159 
cavitation noise measurement, 155- 
156 

comparison with polarized light 
flume, 27 

corrections to test data, 277-278 
directivity pattern of hydrophone 
system, 155-156 
focussing reflectors, 155-156 
noise from circuit variables, 157 
purpose, 1 

Water tunnel, free-surface, 52-56 
air separator, 53-56 
comparison with polarized light 
flume, 27 
purpose, 5-6 
working section, 53 
Water tunnel, high-speed, 4, 7-27 
air removal and flow straightening, 
14 

balance system, 16-18, 21 
circulating pump and drive, 11 
comparison with polarized light 
flume, 27 
^ng circuit, 16 
mometer, 12 

components, 7-8 
flow circuit, 1 1 
JEDT nozzle, 14 

operating techniques, 24-27 
operating variables, 25 
pressure distribution measuring 
equipment, 21-22 
pressure gauges, 19-21 
pressure regulating circuits, 15-16 
purpose and specifications, 7-1 1 
speed control, 12-13 
tests, 25-27 

types of measurements, 4 
working section, 15 
Water-borne torpedoes, 
dimensions, 203 
Mark 14 and 15 series, 207 
Mark 26 torpedo, 208-209 
Westinghouse, 205-206 


235- 


X-42 dei)th charge, 245-248 


Yaw angle, definition, 275 


- 4 






f <*■ 


*^£..7 . Cs I 

J;\ ^ • > 

f 


>-r^\ 

. ifc ^ * 


» l l ‘S ’ *’ /• 

* .... .V* . » ■ , . ''f';'‘ ’'^*^ 1 :' •* *•■■ 1 “ 

* V • j ' .1 * * ■ 1 -.• * 

>••.•-••■ f #■ »• < . '. V ■ . 


,»4 


. ■ 

• •• ; *1 -' 





'^ - 


«> 



# * 


, . ‘';tn . ,. ' „. 

V,. 


. ' - / ^ - ■’ i’ •» . ’-i; ■ir^i ' ■*■. V ^ ^-'1 *«■ /■ .'^'3 

■r - . ,••■ ,. ■m4& 




fV.. Ji ^ 

i ’ . , 

%. V 


j i 

T r^ .V‘*; -! 

i’.r' / c , 
..-1/ ^ ^ < * 


V* jj -r'l j 


I _ 

I 


. 4 f 




.fc 4 


• '■• .- 


I « 



a -‘ ■■■’ 




♦ - I • M ^ , 

<«« } ■■ I ^ - 

»< • J . ^ 

I.V 


■r >: 


> t 

- Jf^ 


:^m 


i • 






.-4- 



* . ''’m- > . t'“ *' * * ■ ' 

V ■ W » ■ :* . *V '/- ' • 't* , *■ ■ . 

' ■■ .V.vf..- •; -'..^.i*,....-- ., 


Vs 






,/jf? , . ' ;«#^ '• '• te'" \-^ 

^i4|^ •* '• iV. ^ i 2 ■w'’^i-'® * ‘ 

^ . ■"■■ ,v7 

. -ja • * I •■? 

:S-» 'T‘ ;*' 


.li •.' - •, . 

f 4 k * ^ _ * 


^ * * * • .. 

^ftr w •' i*« 1 ^- '■ 

l■■Jta';i;'i' r. J'. . '.^ 


■ -.IKJ. V • *^" 





,;i 


i 




T. 

••■ V 


*k/Y • *> 

^^» ‘> *■** 1/- ”* > ' ♦ 

' '■ -^* ._ . 


<»v 

A-v IV. ♦ 

^ ’ll ^ L* • - 




T a 






■ • v’-'. - 





T t.. y - 4-J..0 i 4 


- > j 3 


1 .. 



4 4* « * ^ ^ * 

■"/'■. 'Jet. '.-•, 


V V. 

• ^ 
' 1^ 


:*^*-r: 


WhiD^^C. ^ \ t •■i^r jS^>^^Ar ” ^ 

^r.. -r ... 4/|SC-’*M 

b#C"* : ;• • -v ' ■ ^lOi 


■♦ •/ . «■¥ , '<i 4 * m y I.' ' 
fv I * r „ rA 

ETa^-^ ., 


1 

< 



■> ’ ^ . ■ ^ 4k 

a * ■ 


t' * ■ 

• » 


r-y/' '-V'i*: / . ,•■ 

« ' • ... . ' i «Fi iTHiflM 


. «• 


> ' ■ \ *^ 

^ a } ’’S 


ti -4H 




.ii-. 






* 

’ < 


> * 


.rL*. 


. i 


^ > •# -t- ► 

.--•v 


't-;- ‘•4., 

..,. ^ ^ vv. V..' : 

S 4 r* fi##^ ' - ■'- < •^* 

-J _ ,'-. . . t' •".V 




P<r , K: 
Hi’’ -IJ 


.T>- 




i 


'V, 


'* . 4 . ‘- 


f 

: t 


> % 4%-^ 


41 

J 




V> ■ \*--t ■ -s 

^ nBii^lbA‘'V \rl '.a^ .*. 


V 




I*;/ •'-■ 


.^V ‘ *4 


>- 

n 


• *1 . vt 


'A 








» ' i 

■ t. ..Lm .,.;‘_ 

■ i.' iM.i r ' ’• 

f>‘*’ V 

‘■u • - - 

',vi4' Jf*' ‘JUr-* 'i 

■4- 



I, .'"^l-. ! V-.. 

4 » ^- ‘ ..'■*• • 

t , ^ ’ V -< I 


• _>• 




'i > • 




► f 



H- '/ . M 

V ‘ 

>1.^ ^V*, 

/i”- 

S'" *1. f » i-? I .. 


K a ' _J « 4»^.I ♦ 


SI 


lAi?» 




^ ' a " I*" 


■■i' 

• J 4 k * 



pyi 4- , • ^ »i '* 


'biSVkr.' 


t* 

X 



t 

h 

* a - * 

f. ¥4 r - 





T 1 * F 4 

’I 


A 




»l? a;&l:v :&.' ^ '-s.- 







i tf 








rss, ' .--v. . - 

®— 'jg -'t? ' ~ 


56 ; ■"■>•. • 


■•ijn ' 

-•H > • 





I w* '■ i.if r!ii -d ^ ^ i I 


fl'v • 




. « . 
I'v 




■ ■ u - v^ -’ ' ■ » ' ■• "^r.w . K* *’■ .■ ) 


j_ V •*• ^ V •*■ *t 

■^■''i’j'^ ■ ' ■■■ 

**.*,. .. • kii 


#*■• I 




if 




A*? 


kifv / 



^ t- 

kT 

V ■■ 

/A 




t- 

% 7 A' 

‘ i^t 
(»-*'** 

^ • p i-f ' 

' r 

* 

»' 


1 

' 4 

< ' 1 

'•V' 7, 
'” . 

. 

H 

«- 

• 

V .1 4 • 

•i4 

7W 




.,\ -I' 


n- S*' : 

i ' - •*• 


iv v'b ■ ■ ■ ■ ' 

..^■. A.. 

. ’ , A.' 

; * ■ , ■ 

-■' .Xv- 

#/,. . 

■ * ■■,'■ Js ♦ 



, . 1 . .. - . I ^ , 

Vvki. 7 ^,- 

« . • 






Ll&M..;v5ijyt?, - ■ ,'A/ ■ 

•* I V -■■' ' '- i 4 :'*‘’ •^' '■ 

If i WmiW t A A >*■•■. “[ Jp '0 



i ^ 


' •. I. ’ 

* ., T^f^W 

■ _ i 


py-v, ■ ■' IB- HlitT. :».* =■“' 7i ;•>. vti*- L ..■ A-A 





.V'V 




yf.v 
















i' '5 




'm 


1. 




m 




i ‘V/ , 






M 


ri'i>i 






Sll 


. 'i 1*1 








V 


M' 






j • 





?r‘V 




fa. 






'I^f 4 


V /' ' '', 


A 


^^1-3 


tl * I 


^0.' 


'V^y 


,v< 


Ai f !:* 




li -v S A I 


/• 


A V>4 


''y .' *r- ■*•' '!i*" . * •’*' 

- .. . t “ ' 'T' ■ » - 3 ^ ,'i,/r. 


rt.' 


« V 


i ^ 


-.'I 






♦>< 


,« / 




tJL 


J) 




:«v 




M j 


u • \1 




,f:v;i 








'\!i 


,Ov # 


» i il 




A 




iv-' 




) ' 


M 




- « 


I ^ 


./r. 




'<1 


V®>. 


A'. 










J' 









m 




> / 


•■j f 






‘•vr. 


i 




Wi 




'tel 




» ■ ' s. 


m 


|V^ 


f ';/'v* ''U:’':. 

'' -/V ' 




f' V 







- ■ 


l/’ \t' I ■ 




W' 


.t f 












kV 






'Mi^l 


^H?' 






.F, 


*».!• 




rA-Vt 


r-J" ki 


t .• 








k'iflUi 




■i V' 


1 


’-Vt' 





» • 


w 




.D*' J-Vr y ,»- 

•’ T ’ ‘ ’ * 


. y 








>- 




? r 








•>; 1 


, 'v'' '- 




J&J 




• ’ ., . 4 


,:rW’ 


u» 










a ■ 











»”‘S .'./^i' 






bl ^ ./■*' 




IWj; 


.'fN-* 




P'1' I 


1^ 


I V 'u 1 




V ^ • 








Uv 




:t 




WUI 


Vv'^' 


■i • .f{ 


N 


.•’. ak' '* 


• k.M 






I * 1 

:; -yi 

'^:V■,^'<. . ’ I 
^ . " • j 


1. 

_' < r 


fhtl.V " 










rAL* :;'* 


,1B-* 


■w- 


I 1 -a 41 


^ ' i ' 




lu *« 


y ' ‘ . ■ \l 






'/I 


.a' 


* ’ i 


W.' 


‘IL 






Vi 


/V 






a ■'f. 


t",, 

SWSP» 






CT 






W- 


ir*’H 


fc- 


% 


•»< *; 


* ‘4; 




Vw>i 


Xi/: 


:if'' 






■ ■'•*. 


'V/.t 


V^’ 


H+ 


' r- ,a\ 




Ijilii!' 




{ # 


2 jjy^i 


vj 


♦ -4' 


r.jj 






^ •;> 


A* ' 

i ^ 


i 4 j 


1 • 3* 






V.\^A-V^r/ 




V, 


> 


.m 




1 i ‘.i 




V f. 




(AV 


v» 


K- 


19 




f* 


• • ■ 


4 Ik' 






^ I*. 


a' •v.>&'u 


Tl 




^/k: 






Lb*i 


1} 


r'ti 




•i/4 


■ <* V' 

, " ■» » 'VV- 


f '> 






rV / ' 




M 


iistl 








a,- ' ^'vv i 


» / 






>*^-' \ 


.4 • ' 








;:^w 


^i 


















^mrnty aeci 
Ot I 


of 


l! 


I960 


ttro 


I' 




